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    <div class="section end-of-chapter" id="fwk-redden-ch09_s05" version="5.0" lang="en">
    <h2 class="title editable block">
<span class="title-prefix">9.5</span> Review Exercises and Sample Exam</h2>
    <div class="qandaset block" id="fwk-redden-ch09_s05_qs01" defaultlabel="number">
        <h3 class="title">Review Exercises</h3>
        <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd01">
            <h3 class="title">Introduction to Sequences and Series</h3>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd01_qd01">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p01"><strong class="emphasis bold">Find the first 5 terms of the sequence as well as the 30<sup class="superscript">th</sup> term.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa01">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p02"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1109" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>5</mn><mi>n</mi><mo>−</mo><mn>3</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa02">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p04"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1111" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mn>4</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa03">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p06"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1113" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mn>10</mn><mi>n</mi></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa04">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p08"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1115" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>3</mn><mi>n</mi></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa05">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p10"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1117" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup><msup><mrow><mrow><mo>(</mo><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa06">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p12"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1119" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa07">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p14"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1125" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mi>n</mi></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa08">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p16"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1131" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd01_qd02" start="9">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p18"><strong class="emphasis bold">Find the first 5 terms of the sequence.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa09">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p19"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1133" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mrow><mi>n</mi><msup><mi>x</mi><mi>n</mi></msup></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa10">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p21"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1135" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup></mrow><mi>n</mi></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa11">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p23"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1137" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><msup><mi>x</mi><mrow><mn>2</mn><mi>n</mi></mrow></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa12">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p25"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1139" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn><mi>x</mi></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa13">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p27"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1141" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><mn>5</mn></mrow></math></span> where <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1142" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>0</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa14">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p29"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1143" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>4</mn><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><mn>1</mn></mrow></math></span> where <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1144" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>2</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa15">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p31"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1145" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub><mo>−</mo><mn>3</mn><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></math></span> where <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1146" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>0</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1147" display="inline"><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><mn>3</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa16">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p33"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1148" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>5</mn><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub><mo>−</mo><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></math></span> where <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1149" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1150" display="inline"><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd01_qd03" start="17">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p35"><strong class="emphasis bold">Find the indicated partial sum.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa17">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p36">1, 4, 7, 10, 13,…; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1151" display="inline"><mrow><msub><mi>S</mi><mn>5</mn></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa18">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p38">3, 1, −1, −3, −5,…; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1152" display="inline"><mrow><msub><mi>S</mi><mn>5</mn></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa19">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p40">−1, 3, −5, 7, −9,…; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1153" display="inline"><mrow><msub><mi>S</mi><mn>4</mn></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa20">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p42"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1154" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup><msup><mi>n</mi><mn>2</mn></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1155" display="inline"><mrow><msub><mi>S</mi><mn>4</mn></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa21">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p44"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1156" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mn>3</mn><msup><mrow><mrow><mo>(</mo><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1157" display="inline"><mrow><msub><mi>S</mi><mn>4</mn></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa22">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p46"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1158" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1159" display="inline"><mrow><msub><mi>S</mi><mn>4</mn></msub></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd01_qd04" start="23">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p48"><strong class="emphasis bold">Evaluate.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa23">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1161" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mn>6</mn></munderover><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>k</mi></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa24">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1162" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mn>4</mn></munderover><mrow><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mi>k</mi></msup><mn>3</mn><msup><mi>k</mi><mn>2</mn></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa25">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1163" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>3</mn></munderover><mrow><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mi>n</mi></mfrac></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa26">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1165" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><mrow><mn>5</mn><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa27">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1166" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>4</mn></mrow><mn>8</mn></munderover><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><mi>k</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa28">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1167" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mo>−</mo><mn>2</mn></mrow><mn>2</mn></munderover><mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mi>k</mi></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
            </ol>
        </ol>
        <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd02">
            <h3 class="title">Arithmetic Sequences and Series</h3>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd02_qd01" start="29">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p61"><strong class="emphasis bold">Write the first 5 terms of the arithmetic sequence given its first term and common difference. Find a formula for its general term.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa29">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p62"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1169" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>6</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1170" display="inline"><mrow><mi>d</mi><mo>=</mo><mn>5</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa30">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p64"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1172" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>5</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1173" display="inline"><mrow><mi>d</mi><mo>=</mo><mn>7</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa31">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p66"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1175" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>5</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1176" display="inline"><mrow><mi>d</mi><mo>=</mo><mo>−</mo><mn>3</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa32">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p68"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1178" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1179" display="inline"><mrow><mi>d</mi><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa33">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p70"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1184" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1185" display="inline"><mrow><mi>d</mi><mo>=</mo><mo>−</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa34">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p72"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1191" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>3.6</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1192" display="inline"><mrow><mi>d</mi><mo>=</mo><mn>1.2</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa35">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p74"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1194" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>7</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1195" display="inline"><mrow><mi>d</mi><mo>=</mo><mn>0</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa36">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p76"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1197" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>1</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1198" display="inline"><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd02_qd02" start="37">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p78"><strong class="emphasis bold">Given the terms of an arithmetic sequence, find a formula for the general term.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa37">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p79">10, 20, 30, 40, 50,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa38">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p81">−7, −5, −3, −1, 1,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa39">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p83">−2, −5, −8, −11, −14,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa40">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p85"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1203" display="inline"><mrow><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></math></span>, 0, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1204" display="inline"><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1205" display="inline"><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></math></span>, 1,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa41">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p87"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1207" display="inline"><mrow><msub><mi>a</mi><mn>4</mn></msub><mo>=</mo><mn>11</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1208" display="inline"><mrow><msub><mi>a</mi><mn>9</mn></msub><mo>=</mo><mn>26</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa42">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p89"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1210" display="inline"><mrow><msub><mi>a</mi><mn>5</mn></msub><mo>=</mo><mo>−</mo><mn>5</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1211" display="inline"><mrow><msub><mi>a</mi><mrow><mn>10</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>15</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa43">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p91"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1213" display="inline"><mrow><msub><mi>a</mi><mn>6</mn></msub><mo>=</mo><mn>6</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1214" display="inline"><mrow><msub><mi>a</mi><mrow><mn>24</mn></mrow></msub><mo>=</mo><mn>15</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa44">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p93"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1216" display="inline"><mrow><msub><mi>a</mi><mn>3</mn></msub><mo>=</mo><mo>−</mo><mn>1.4</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1217" display="inline"><mrow><msub><mi>a</mi><mn>7</mn></msub><mo>=</mo><mn>1</mn></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd02_qd03" start="45">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p95"><strong class="emphasis bold">Calculate the indicated sum given the formula for the general term of an arithmetic sequence.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa45">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p96"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1219" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>4</mn><mi>n</mi><mo>−</mo><mn>3</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1220" display="inline"><mrow><msub><mi>S</mi><mrow><mn>60</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa46">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p98"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1221" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>9</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1222" display="inline"><mrow><msub><mi>S</mi><mrow><mn>35</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa47">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p100"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1223" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mi>n</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1224" display="inline"><mrow><msub><mi>S</mi><mrow><mn>15</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa48">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p102"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1226" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mi>n</mi><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1227" display="inline"><mrow><msub><mi>S</mi><mrow><mn>20</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa49">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p104"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1228" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>1.8</mn><mi>n</mi><mo>−</mo><mn>4.2</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1229" display="inline"><mrow><msub><mi>S</mi><mrow><mn>45</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa50">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p106"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1230" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mn>6.5</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1231" display="inline"><mrow><msub><mi>S</mi><mrow><mn>35</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd02_qd04" start="51">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p108"><strong class="emphasis bold">Evaluate.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa51">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1232" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>22</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mn>7</mn><mi>n</mi><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa52">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1233" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>100</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><mn>4</mn><mi>n</mi></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa53">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1234" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>35</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>n</mi></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa54">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1235" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>30</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa55">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1237" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>40</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mn>2.3</mn><mi>n</mi><mo>−</mo><mn>1.1</mn></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa56">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1238" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>300</mn></mrow></munderover><mi>n</mi></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa57">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p121">Find the sum of the first 175 positive odd integers.</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa58">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p123">Find the sum of the first 175 positive even integers.</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa59">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p125">Find all arithmetic means between <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1239" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1240" display="inline"><mrow><msub><mi>a</mi><mn>5</mn></msub><mo>=</mo><mo>−</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa60">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p127">Find all arithmetic means between <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1243" display="inline"><mrow><msub><mi>a</mi><mn>3</mn></msub><mo>=</mo><mo>−</mo><mn>7</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1244" display="inline"><mrow><msub><mi>a</mi><mn>7</mn></msub><mo>=</mo><mn>13</mn></mrow><mo>.</mo></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa61">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p129">A 5-year salary contract offers $58,200 for the first year with a $4,200 increase each additional year. Determine the total salary obligation over the 5-year period.</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa62">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p131">The first row of seating in a theater consists of 10 seats. Each successive row consists of four more seats than the previous row. If there are 14 rows, how many total seats are there in the theater?</p>
                    </div>
                </li>
            </ol>
        </ol>
        <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd03">
            <h3 class="title">Geometric Sequences and Series</h3>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd03_qd01" start="63">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p133"><strong class="emphasis bold">Write the first 5 terms of the geometric sequence given its first term and common ratio. Find a formula for its general term.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa63">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p134"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1245" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>5</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1246" display="inline"><mrow><mi>r</mi><mo>=</mo><mn>2</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa64">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p136"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1248" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>3</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1249" display="inline"><mrow><mi>r</mi><mo>=</mo><mo>−</mo><mn>2</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa65">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p138"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1251" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>1</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1252" display="inline"><mrow><mi>r</mi><mo>=</mo><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa66">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p140"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1258" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>4</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1259" display="inline"><mrow><mi>r</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa67">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p142"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1265" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mn>1.2</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1266" display="inline"><mrow><mi>r</mi><mo>=</mo><mn>0.2</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa68">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p144"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1268" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>5.4</mn></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1269" display="inline"><mrow><mi>r</mi><mo>=</mo><mo>−</mo><mn>0.1</mn></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd03_qd02" start="69">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p146"><strong class="emphasis bold">Given the terms of a geometric sequence, find a formula for the general term.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa69">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p147">4, 40, 400,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa70">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p149">−6, −30, −150,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa71">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p151">6, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1273" display="inline"><mrow><mfrac><mn>9</mn><mn>2</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1274" display="inline"><mrow><mfrac><mrow><mn>27</mn></mrow><mn>8</mn></mfrac></mrow></math></span>,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa72">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p153">1, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1276" display="inline"><mrow><mfrac><mn>3</mn><mn>5</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1277" display="inline"><mrow><mfrac><mn>9</mn><mrow><mn>25</mn></mrow></mfrac></mrow></math></span>,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa73">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p155"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1279" display="inline"><mrow><msub><mi>a</mi><mn>4</mn></msub><mo>=</mo><mo>−</mo><mn>4</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1280" display="inline"><mrow><msub><mi>a</mi><mn>9</mn></msub><mo>=</mo><mn>128</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa74">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p157"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1282" display="inline"><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1283" display="inline"><mrow><msub><mi>a</mi><mn>5</mn></msub><mo>=</mo><mo>−</mo><mn>64</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa75">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p159"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1285" display="inline"><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1286" display="inline"><mrow><msub><mi>a</mi><mn>5</mn></msub><mo>=</mo><mo>−</mo><mfrac><mrow><mn>625</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa76">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p161"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1288" display="inline"><mrow><msub><mi>a</mi><mn>3</mn></msub><mo>=</mo><mn>50</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1289" display="inline"><mrow><msub><mi>a</mi><mn>6</mn></msub><mo>=</mo><mo>−</mo><mn>6,250</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa77">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p163">Find all geometric means between <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1291" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1292" display="inline"><mrow><msub><mi>a</mi><mn>4</mn></msub><mo>=</mo><mn>64</mn></mrow><mo>.</mo></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa78">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p165">Find all geometric means between <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1293" display="inline"><mrow><msub><mi>a</mi><mn>3</mn></msub><mo>=</mo><mn>6</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1294" display="inline"><mrow><msub><mi>a</mi><mn>6</mn></msub><mo>=</mo><mn>162</mn></mrow><mo>.</mo></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd03_qd03" start="79">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p167"><strong class="emphasis bold">Calculate the indicated sum given the formula for the general term of a geometric sequence.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa79">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p168"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1295" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>3</mn><msup><mrow><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1296" display="inline"><mrow><msub><mi>S</mi><mn>6</mn></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa80">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p170"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1297" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mn>5</mn><msup><mrow><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1298" display="inline"><mrow><msub><mi>S</mi><mrow><mn>10</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa81">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p172"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1299" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1300" display="inline"><mrow><msub><mi>S</mi><mrow><mn>14</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa82">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p174"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1301" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1302" display="inline"><mrow><msub><mi>S</mi><mrow><mn>12</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa83">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p176"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1303" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>8</mn><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1304" display="inline"><mrow><msub><mi>S</mi><mn>8</mn></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa84">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p178"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1306" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1307" display="inline"><mrow><msub><mi>S</mi><mrow><mn>10</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd03_qd04" start="85">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p180"><strong class="emphasis bold">Evaluate.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa85">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1308" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>10</mn></mrow></munderover><mrow><mn>3</mn><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa86">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1309" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>9</mn></munderover><mrow><mo>−</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa87">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1311" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover><mrow><mo>−</mo><mn>3</mn><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa88">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1312" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>4</mn><mn>5</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa89">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1314" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa90">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1315" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa91">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p193">After the first year of operation, the value of a company van was reported to be $40,000. Because of depreciation, after the second year of operation the van was reported to have a value of $32,000 and then $25,600 after the third year of operation. Write a formula that gives the value of the van after the <em class="emphasis">n</em>th year of operation. Use it to determine the value of the van after 10 years of operation.</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa92">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p195">The number of cells in a culture of bacteria doubles every 6 hours. If 250 cells are initially present, write a sequence that shows the number of cells present after every 6-hour period for one day. Write a formula that gives the number of cells after the <em class="emphasis">n</em>th 6-hour period.</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa93">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p197">A ball bounces back to one-half of the height that it fell from. If dropped from 32 feet, approximate the total distance the ball travels.</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa94">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p199">A structured settlement yields an amount in dollars each year <em class="emphasis">n</em> according to the formula <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1320" display="inline"><mrow><msub><mi>p</mi><mi>n</mi></msub><mo>=</mo><mn>12,500</mn><msup><mrow><mrow><mo>(</mo><mrow><mn>0.75</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow><mo>.</mo></math></span> What is the total value of a 10-year settlement?</p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd03_qd05" start="95">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p201"><strong class="emphasis bold">Classify the sequence as arithmetic, geometric, or neither.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa95">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p202">4, 9, 14,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa96">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p204">6, 18, 54,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa97">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p206">−1, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1323" display="inline"><mrow><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span>, 0,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa98">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p208">10, 30, 60,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa99">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p210">0, 1, 8,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa100">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p212">−1, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1325" display="inline"><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1326" display="inline"><mrow><mo>−</mo><mfrac><mn>4</mn><mn>9</mn></mfrac></mrow></math></span>,…</p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd03_qd06" start="101">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p214"><strong class="emphasis bold">Evaluate.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa101">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1328" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>4</mn></munderover><mrow><msup><mi>n</mi><mn>2</mn></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa102">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1329" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>4</mn></munderover><mrow><msup><mi>n</mi><mn>3</mn></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa103">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1330" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>32</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn><mi>n</mi><mo>+</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa104">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1331" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover><mrow><mo>−</mo><mn>2</mn><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>5</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa105">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1333" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>8</mn></munderover><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mi>n</mi></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa106">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1334" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>46</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>n</mi><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa107">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1336" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>22</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mo>−</mo><mi>n</mi></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa108">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1337" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>31</mn></mrow></munderover><mrow><mn>2</mn><mi>n</mi></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa109">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1338" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>28</mn></mrow></munderover><mn>3</mn></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa110">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1339" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>30</mn></mrow></munderover><mrow><mn>3</mn><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa111">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1340" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>31</mn></mrow></munderover><mrow><mn>3</mn><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
            </ol>
        </ol>
        <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd04">
            <h3 class="title">Binomial Theorem</h3>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd04_qd01" start="112">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p237"><strong class="emphasis bold">Evaluate.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa112">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p238"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1341" display="inline"><mrow><mn>8</mn><mo>!</mo></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa113">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p240"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1342" display="inline"><mrow><mn>11</mn><mo>!</mo></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa114">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p242"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1343" display="inline"><mrow><mfrac><mrow><mn>10</mn><mo>!</mo></mrow><mrow><mn>2</mn><mo>!</mo><mn>6</mn><mo>!</mo></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa115">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p244"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1344" display="inline"><mrow><mfrac><mrow><mn>9</mn><mo>!</mo><mn>3</mn><mo>!</mo></mrow><mrow><mn>8</mn><mo>!</mo></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa116">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p246"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1345" display="inline"><mrow><mfrac><mrow><mrow><mo>(</mo><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow><mo>)</mo></mrow><mo>!</mo></mrow><mrow><mi>n</mi><mo>!</mo></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa117">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p248"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1347" display="inline"><mrow><mfrac><mrow><mrow><mo>(</mo><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow><mo>!</mo></mrow><mrow><mrow><mo>(</mo><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>!</mo></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd04_qd02" start="118">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p250"><strong class="emphasis bold">Calculate the indicated binomial coefficient.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa118">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1349" display="block"><mrow><mrow><mo>(</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa119">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1350" display="block"><mrow><mrow><mo>(</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa120">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1351" display="block"><mrow><mrow><mo>(</mo><mtable columnspacing="0.1em"><mtr><mtd><mn>10</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa121">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1352" display="block"><mrow><mrow><mo>(</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mn>11</mn></mtd></mtr><mtr><mtd><mn>10</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa122">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1353" display="block"><mrow><mrow><mo>(</mo><mtable columnspacing="0.1em"><mtr><mtd><mn>12</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa123">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1354" display="block"><mrow><mrow><mo>(</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mi>n</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>n</mi><mo>−</mo><mn>1</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa124">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1356" display="block"><mrow><mrow><mo>(</mo><mtable columnspacing="0.1em"><mtr><mtd><mi>n</mi></mtd></mtr><mtr><mtd><mi>n</mi><mo>−</mo><mn>2</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow></math></span>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs01_qd04_qd03" start="125">
                <p class="para" id="fwk-redden-ch09_s05_qs01_p265"><strong class="emphasis bold">Expand using the binomial theorem.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa125">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p266"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1358" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow><mn>3</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa126">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p268"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1360" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>9</mn></mrow><mo>)</mo></mrow></mrow><mn>3</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa127">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p270"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1362" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mi>y</mi><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mn>4</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa128">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p272"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1364" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>y</mi><mo>+</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mn>4</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa129">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p274"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1366" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi></mrow><mo>)</mo></mrow></mrow><mn>5</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa130">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p276"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1368" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mi>y</mi></mrow><mo>)</mo></mrow></mrow><mn>5</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa131">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p278"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1370" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>u</mi><mo>−</mo><mi>v</mi></mrow><mo>)</mo></mrow></mrow><mn>6</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa132">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p280"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1372" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>u</mi><mo>+</mo><mi>v</mi></mrow><mo>)</mo></mrow></mrow><mn>6</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa133">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p282"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1374" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mn>4</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa134">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs01_p284"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1376" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>−</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mn>4</mn></msup></mrow></math></span></p>
                    </div>
                </li>
            </ol>
        </ol>
    </div>
    <div class="qandaset block" id="fwk-redden-ch09_s05_qs01_ans" defaultlabel="number">
        <h3 class="title">Answers</h3>
        <ol class="qandadiv">
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa01_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p03_ans">2, 7, 12, 17, 22; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1110" display="inline"><mrow><msub><mi>a</mi><mrow><mn>30</mn></mrow></msub><mo>=</mo><mn>147</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa02_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa03_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p07_ans">−10, −20, −30, −40, −50; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1114" display="inline"><mrow><msub><mi>a</mi><mrow><mn>30</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>300</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa04_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa05_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p11_ans">−1, 0, −1, 4, −9; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1118" display="inline"><mrow><msub><mi>a</mi><mrow><mn>30</mn></mrow></msub><mo>=</mo><mn>784</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa06_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa07_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p15_ans">3, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1126" display="inline"><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1127" display="inline"><mrow><mfrac><mn>7</mn><mn>3</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1128" display="inline"><mrow><mfrac><mn>9</mn><mn>4</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1129" display="inline"><mrow><mfrac><mrow><mn>11</mn></mrow><mn>5</mn></mfrac></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1130" display="inline"><mrow><msub><mi>a</mi><mrow><mn>30</mn></mrow></msub><mo>=</mo><mfrac><mrow><mn>61</mn></mrow><mrow><mn>30</mn></mrow></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa08_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa09_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p20_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1134" display="inline"><mrow><mfrac><mi>x</mi><mn>3</mn></mfrac><mo>,</mo><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>5</mn></mfrac><mo>,</mo><mfrac><mrow><mn>3</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mn>7</mn></mfrac><mo>,</mo><mfrac><mrow><mn>4</mn><msup><mi>x</mi><mn>4</mn></msup></mrow><mn>9</mn></mfrac><mo>,</mo><mfrac><mrow><mn>5</mn><msup><mi>x</mi><mn>5</mn></msup></mrow><mrow><mn>11</mn></mrow></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa10_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa11_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p24_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1138" display="inline"><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><mn>4</mn><msup><mi>x</mi><mn>4</mn></msup><mo>,</mo><mn>8</mn><msup><mi>x</mi><mn>6</mn></msup><mo>,</mo><mn>16</mn><msup><mi>x</mi><mn>8</mn></msup><mo>,</mo><mn>32</mn><msup><mi>x</mi><mrow><mn>10</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa12_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa13_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p28_ans">0, 5, 10, 15, 20</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa14_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa15_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p32_ans">0, −3, 9, −30, 99</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa16_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa17_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p37_ans">35</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa18_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa19_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p41_ans">−5</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa20_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa21_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p45_ans">−18</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa22_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa23_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p50_ans">−36</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa24_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa25_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p54_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1164" display="inline"><mrow><mfrac><mrow><mn>29</mn></mrow><mn>6</mn></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa26_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa27_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p58_ans">135</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa28_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
        </ol>
        <ol class="qandadiv" start="29">
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa29_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p63_ans">6, 11, 16, 21, 26; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1171" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>5</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa30_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa31_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p67_ans">5, 2, −1, −4, −7; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1177" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>8</mn><mo>−</mo><mn>3</mn><mi>n</mi></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa32_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa33_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p71_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1186" display="inline"><mrow><mo>−</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1187" display="inline"><mrow><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1188" display="inline"><mrow><mo>−</mo><mfrac><mn>9</mn><mn>4</mn></mfrac></mrow></math></span>, −3, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1189" display="inline"><mrow><mo>−</mo><mfrac><mrow><mn>15</mn></mrow><mn>4</mn></mfrac></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1190" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>n</mi></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa34_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa35_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p75_ans">7, 7, 7, 7, 7; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1196" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>7</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa36_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa37_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p80_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1200" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>10</mn><mi>n</mi></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa38_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa39_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p84_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1202" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>1</mn><mo>−</mo><mn>3</mn><mi>n</mi></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa40_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa41_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p88_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1209" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa42_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa43_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p92_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1215" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>n</mi><mo>+</mo><mn>3</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa44_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa45_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p97_ans">7,140</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa46_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa47_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p101_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1225" display="inline"><mrow><mfrac><mrow><mn>33</mn></mrow><mn>2</mn></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa48_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa49_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p105_ans">1,674</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa50_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa51_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p110_ans">1,661</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa52_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa53_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p114_ans">420</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa54_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa55_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p118_ans">1,842</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa56_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa57_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p122_ans">30,625</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa58_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa59_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p126_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1241" display="inline"><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></math></span>, 0, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1242" display="inline"><mrow><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa60_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa61_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p130_ans">$333,000</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa62_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
        </ol>
        <ol class="qandadiv" start="63">
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa63_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p135_ans">5, 10, 20, 40, 80; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1247" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>5</mn><msup><mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa64_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa65_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p139_ans">1, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1253" display="inline"><mrow><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1254" display="inline"><mrow><mfrac><mn>9</mn><mn>4</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1255" display="inline"><mrow><mo>−</mo><mfrac><mrow><mn>27</mn></mrow><mn>8</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1256" display="inline"><mrow><mfrac><mrow><mn>81</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1257" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa66_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa67_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p143_ans">1.2, 0.24, 0.048, 0.0096, 0.00192; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1267" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>1.2</mn><msup><mrow><mrow><mo>(</mo><mrow><mn>0.2</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa68_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa69_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p148_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1271" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>4</mn><msup><mrow><mrow><mo>(</mo><mrow><mn>10</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa70_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa71_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p152_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1275" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>6</mn><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa72_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa73_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p156_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1281" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa74_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa75_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p160_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1287" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa76_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa77_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p164_ans">4, −16</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa78_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa79_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p169_ans">4,095</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa80_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa81_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p173_ans">16,383</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa82_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa83_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p177_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1305" display="inline"><mrow><mfrac><mrow><mn>255</mn></mrow><mrow><mn>128</mn></mrow></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa84_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa85_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p182_ans">2,516,580</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa86_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa87_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p186_ans">−6</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa88_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa89_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p190_ans">No sum</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa90_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa91_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p194_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1317" display="inline"><mrow><msub><mi>v</mi><mi>n</mi></msub><mo>=</mo><mn>40,000</mn><msup><mrow><mrow><mo>(</mo><mrow><mn>0.8</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1318" display="inline"><mrow><msub><mi>v</mi><mrow><mn>10</mn></mrow></msub><mo>=</mo><mi>$</mi><mn>5,368.71</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa92_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa93_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p198_ans">96 feet</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa94_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa95_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p203_ans">Arithmetic; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1321" display="inline"><mrow><mi>d</mi><mo>=</mo><mn>5</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa96_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa97_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p207_ans">Arithmetic; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1324" display="inline"><mrow><mi>d</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa98_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa99_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p211_ans">Neither</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa100_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa101_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p216_ans">30</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa102_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa103_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p220_ans">−1,952</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa104_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa105_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p224_ans">1,640</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa106_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa107_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p228_ans">−187</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa108_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa109_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p232_ans">84</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa110_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa111_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p236_ans">3</p>
                </div>
            </li>
        </ol>
        <ol class="qandadiv" start="112">
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa112_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa113_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p241_ans">39,916,800</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa114_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa115_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p245_ans">54</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa116_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa117_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p249_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1348" display="inline"><mrow><mfrac><mn>1</mn><mrow><mi>n</mi><mrow><mo>(</mo><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa118_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa119_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p254_ans">56</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa120_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa121_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p258_ans">11</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa122_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa123_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p262_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1355" display="inline"><mrow><mfrac><mrow><mi>n</mi><mrow><mo>(</mo><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa124_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa125_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p267_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1359" display="inline"><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>21</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>147</mn><mi>x</mi><mo>+</mo><mn>343</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa126_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa127_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p271_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1363" display="inline"><mrow><mn>16</mn><msup><mi>y</mi><mn>4</mn></msup><mo>−</mo><mn>96</mn><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>216</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>216</mn><mi>y</mi><mo>+</mo><mn>81</mn></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa128_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa129_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p275_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1367" display="inline"><mrow><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>10</mn><msup><mi>x</mi><mn>4</mn></msup><mi>y</mi><mo>+</mo><mn>40</mn><msup><mi>x</mi><mn>3</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>80</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>80</mn><mi>x</mi><msup><mi>y</mi><mn>4</mn></msup><mo>+</mo><mn>32</mn><msup><mi>y</mi><mn>5</mn></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa130_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa131_ans">
                <div class="answer">
                    <span class="informalequation"><math xml:id="fwk-redden-ch09_m1371" display="block"><mtable columnspacing="0.1em"><mtr><mtd columnalign="left"><mrow><msup><mi>u</mi><mn>6</mn></msup><mo>−</mo><mn>6</mn><msup><mi>u</mi><mn>5</mn></msup><mi>v</mi><mo>+</mo><mn>15</mn><msup><mi>u</mi><mn>4</mn></msup><msup><mi>v</mi><mn>2</mn></msup><mo>−</mo><mn>20</mn><msup><mi>u</mi><mn>3</mn></msup><msup><mi>v</mi><mn>3</mn></msup></mrow></mtd></mtr><mtr><mtd columnalign="left"><mo>+</mo><mn>15</mn><msup><mi>u</mi><mn>2</mn></msup><msup><mi>v</mi><mn>4</mn></msup><mo>−</mo><mn>6</mn><mi>u</mi><msup><mi>v</mi><mn>5</mn></msup><mo>+</mo><msup><mi>v</mi><mn>6</mn></msup></mtd></mtr></mtable></math></span>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa132_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa133_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs01_p283_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1375" display="inline"><mrow><mn>625</mn><msup><mi>x</mi><mn>8</mn></msup><mo>+</mo><mn>1,000</mn><msup><mi>x</mi><mn>6</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>600</mn><msup><mi>x</mi><mn>4</mn></msup><msup><mi>y</mi><mn>4</mn></msup><mo>+</mo><mn>160</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>6</mn></msup><mo>+</mo><mn>16</mn><msup><mi>y</mi><mn>8</mn></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs01_qa134_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
        </ol>
    </div>
    <div class="qandaset block" id="fwk-redden-ch09_s05_qs02" defaultlabel="number">
        <h3 class="title">Sample Exam</h3>
        <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01">
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01_qd01">
                <p class="para" id="fwk-redden-ch09_s05_qs02_p01"><strong class="emphasis bold">Find the first 5 terms of the sequence.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa01">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p02"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1378" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>6</mn><mi>n</mi><mo>−</mo><mn>15</mn></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa02">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p04"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1379" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>5</mn><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa03">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p06"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1381" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mfrac><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa04">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p08"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1386" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mi>x</mi><mrow><mn>2</mn><mi>n</mi></mrow></msup></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01_qd02" start="5">
                <p class="para" id="fwk-redden-ch09_s05_qs02_p10"><strong class="emphasis bold">Find the indicated partial sum.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa05">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p11"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1388" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mrow><mo>(</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><msup><mi>n</mi><mn>2</mn></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1389" display="inline"><mrow><msub><mi>S</mi><mn>4</mn></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa06">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1390" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mn>5</mn></munderover><mrow><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mi>k</mi></msup><msup><mn>2</mn><mrow><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01_qd03" start="7">
                <p class="para" id="fwk-redden-ch09_s05_qs02_p15"><strong class="emphasis bold">Classify the sequence as arithmetic, geometric, or neither.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa07">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p16">−1, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1392" display="inline"><mrow><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></math></span>, −2,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa08">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p18">1, −6, 36,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa09">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p20"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1393" display="inline"><mrow><mfrac><mn>3</mn><mn>8</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1394" display="inline"><mrow><mo>−</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1395" display="inline"><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></math></span>,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa10">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p22"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1396" display="inline"><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1397" display="inline"><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1398" display="inline"><mrow><mfrac><mn>2</mn><mn>9</mn></mfrac></mrow></math></span>,…</p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01_qd04" start="11">
                <p class="para" id="fwk-redden-ch09_s05_qs02_p24"><strong class="emphasis bold">Given the terms of an arithmetic sequence, find a formula for the general term.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa11">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p25">10, 5, 0, −5, −10,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa12">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p27"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1400" display="inline"><mrow><msub><mi>a</mi><mn>4</mn></msub><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1401" display="inline"><mrow><msub><mi>a</mi><mn>9</mn></msub><mo>=</mo><mn>2</mn></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01_qd05" start="13">
                <p class="para" id="fwk-redden-ch09_s05_qs02_p29"><strong class="emphasis bold">Given the terms of a geometric sequence, find a formula for the general term.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa13">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p30"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1403" display="inline"><mrow><mo>−</mo><mfrac><mn>1</mn><mn>8</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1404" display="inline"><mrow><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span>, −2, −8, −32,…</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa14">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p32"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1406" display="inline"><mrow><msub><mi>a</mi><mn>3</mn></msub><mo>=</mo><mn>1</mn></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1407" display="inline"><mrow><msub><mi>a</mi><mn>8</mn></msub><mo>=</mo><mo>−</mo><mn>32</mn></mrow></math></span></p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01_qd06" start="15">
                <p class="para" id="fwk-redden-ch09_s05_qs02_p34"><strong class="emphasis bold">Calculate the indicated sum.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa15">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p35"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1409" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>5</mn><mo>−</mo><mi>n</mi></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1410" display="inline"><mrow><msub><mi>S</mi><mrow><mn>44</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa16">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p37"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1411" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup></mrow></math></span>; <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1412" display="inline"><mrow><msub><mi>S</mi><mrow><mn>12</mn></mrow></msub></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa17">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1413" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover><mrow><mn>4</mn><msup><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa18">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1415" display="block"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>100</mn></mrow></munderover><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow></mstyle></mrow></math></span>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01_qd07" start="19">
                <p class="para" id="fwk-redden-ch09_s05_qs02_p43"><strong class="emphasis bold">Evaluate.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa19">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p44"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1416" display="inline"><mrow><mfrac><mrow><mn>14</mn><mo>!</mo></mrow><mrow><mn>10</mn><mo>!</mo><mn>6</mn><mo>!</mo></mrow></mfrac></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa20">
                    <div class="question">
                        <span class="informalequation"><math xml:id="fwk-redden-ch09_m1418" display="block"><mrow><mrow><mo>(</mo><mtable columnalign="left" columnspacing="0.1em"><mtr><mtd><mn>9</mn></mtd></mtr><mtr><mtd><mn>7</mn></mtd></mtr></mtable><mo>)</mo></mrow></mrow></math></span>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa21">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p48">Determine the sum of the first 48 positive odd integers.</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa22">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p50">The first row of seating in a theater consists of 14 seats. Each successive row consists of two more seats than the previous row. If there are 22 rows, how many total seats are there in the theater?</p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa23">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p52">A ball bounces back to one-third of the height that it fell from. If dropped from 27 feet, approximate the total distance the ball travels.</p>
                    </div>
                </li>
            </ol>
            <ol class="qandadiv" id="fwk-redden-ch09_s05_qs02_qd01_qd08" start="24">
                <p class="para" id="fwk-redden-ch09_s05_qs02_p54"><strong class="emphasis bold">Expand using the binomial theorem.</strong></p>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa24">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p55"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1419" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>5</mn><mi>y</mi></mrow><mo>)</mo></mrow></mrow><mn>4</mn></msup></mrow></math></span></p>
                    </div>
                </li>
                <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa25">
                    <div class="question">
                        <p class="para" id="fwk-redden-ch09_s05_qs02_p57"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1421" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mi>a</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mn>5</mn></msup></mrow></math></span></p>
                    </div>
                </li>
            </ol>
        </ol>
    </div>
    <div class="qandaset block" id="fwk-redden-ch09_s05_qs02_ans" defaultlabel="number">
        <h3 class="title">Answers</h3>
        <ol class="qandadiv">
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa01_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p03_ans">−9, −3, 3, 9, 15</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa02_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa03_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p07_ans">0, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1382" display="inline"><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1383" display="inline"><mrow><mfrac><mn>2</mn><mn>5</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1384" display="inline"><mrow><mfrac><mn>3</mn><mn>7</mn></mfrac></mrow></math></span>, <span class="inlineequation"><math xml:id="fwk-redden-ch09_m1385" display="inline"><mrow><mfrac><mn>4</mn><mn>9</mn></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa04_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa05_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p12_ans">70</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa06_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa07_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p17_ans">Arithmetic</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa08_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa09_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p21_ans">Geometric</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa10_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa11_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p26_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1399" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mn>15</mn><mo>−</mo><mn>5</mn><mi>n</mi></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa12_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa13_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p31_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1405" display="inline"><mrow><msub><mi>a</mi><mi>n</mi></msub><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mrow><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa14_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa15_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p36_ans">−770</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa16_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa17_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p40_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1414" display="inline"><mrow><mfrac><mn>8</mn><mn>3</mn></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa18_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa19_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p45_ans"><span class="inlineequation"><math xml:id="fwk-redden-ch09_m1417" display="inline"><mrow><mfrac><mrow><mn>1,001</mn></mrow><mrow><mn>30</mn></mrow></mfrac></mrow></math></span></p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa20_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa21_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p49_ans">2,304</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa22_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa23_ans">
                <div class="answer">
                    <p class="para" id="fwk-redden-ch09_s05_qs02_p53_ans">54 feet</p>
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa24_ans" audience="instructoronly">
                <div class="answer" audience="instructoronly" d="" html="http://www.w3.org/1999/xhtml" mml="http://www.w3.org/1998/Math/MathML" xlink="http://www.w3.org/1999/xlink" xml="http://www.w3.org/XML/1998/namespace">
                </div>
            </li>
            <li class="qandaentry" id="fwk-redden-ch09_s05_qs02_qa25_ans">
                <div class="answer">
                    <span class="informalequation"><math xml:id="fwk-redden-ch09_m1422" display="block"><mtable columnspacing="0.1em"><mtr><mtd columnalign="left"><mrow><mn>243</mn><msup><mi>a</mi><mn>5</mn></msup><mo>+</mo><mn>405</mn><msup><mi>a</mi><mn>4</mn></msup><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><mn>270</mn><msup><mi>a</mi><mn>3</mn></msup><msup><mi>b</mi><mn>4</mn></msup></mrow></mtd></mtr><mtr><mtd columnalign="left"><mo>+</mo><mn>90</mn><msup><mi>a</mi><mn>2</mn></msup><msup><mi>b</mi><mn>6</mn></msup><mo>+</mo><mn>15</mn><mi>a</mi><msup><mi>b</mi><mn>8</mn></msup><mo>+</mo><msup><mi>b</mi><mrow><mn>10</mn></mrow></msup></mtd></mtr></mtable></math></span>
                </div>
            </li>
        </ol>
    </div>
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