<!DOCTYPE html> <html> <head> <meta charset="UTF-8"> <link href="shared/bookhub.css" rel="stylesheet" type="text/css"> <title>Review Exercises and Sample Exam</title> </head> <body> <div id=navbar-top class="navbar"> <div class="navbar-part left"> <a href="s12-04-binomial-theorem.html"><img src="shared/images/batch-left.png"></a> <a href="s12-04-binomial-theorem.html">Previous Section</a> </div> <div class="navbar-part middle"> <a href="index.html"><img src="shared/images/batch-up.png"></a> <a href="index.html">Table of Contents</a> </div> <div class="navbar-part right"> </div> </div> <div id="book-content"> <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> </div> </div> <div id=navbar-bottom class="navbar"> <div class="navbar-part left"> <a href="s12-04-binomial-theorem.html"><img src="shared/images/batch-left.png"></a> <a href="s12-04-binomial-theorem.html">Previous Section</a> </div> <div class="navbar-part middle"> <a href="index.html"><img src="shared/images/batch-up.png"></a> <a href="index.html">Table of Contents</a> </div> <div class="navbar-part right"> </div> </div> </div> <script type="text/javascript" src="shared/book.js"></script> <script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=MML_HTMLorMML"></script> </body> </html>