{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Première Cours Suites Partie 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sur la page [https://repl.it/@fredericjunier/PremiereSuitesPartie1](https://repl.it/@fredericjunier/PremiereSuitesPartie1) vous pourrez aussi tester les codes ci-dessous." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Activité 1 : châteaux de cartes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour tout entier naturel $n \\geqslant 1$, on a :\n", "* le nombre de cartes au niveau $n$ vérifie $u_{n}=3n$\n", "* le nombre total de cartes pour construire $n$ niveaux vérifie $v_{n+1}=u_{n+1} + v_{n}$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "def chateau(n):\n", " u = 0\n", " v = 0\n", " for k in range(1, n + 1):\n", " u = u + 3 #u = k * 3\n", " v = v + u\n", " return v" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0, 3, 9, 18, 30, 45, 63, 84]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[chateau(n) for n in range(0, 8)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Activité 2 Modèle d’évolution d’une population" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On a $u_{0}=27500$ étudiants en Septembre 2016.\n", "\n", "En notant $u_{n}$ le nombre d'étudiants en Septembre $2016 + n$, en juin $2016+n+1$, après une perte de $150$ étudiants, on a $u_{n}-150$ étudiants. Puis on a une augmentation de cet effectif, à la rentrée de Septembre, cest-à-dire $1,04(u_{n}-150)=1,04u_{n}-156$ étudiants en Septembre $2016+n+1$. \n", "\n", "Pour tout entier $n \\geqslant 0$, on a donc : $u_{n+1}=1,04u_{n}-156$.\n", "\n", "La capacité maximale de l'établissement est de $33000$. D'après l'algorithme de seuil ci-dessous, à la rentrée de Septembre $2022$, la capacité maximale d'accueil sera dépassée." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def seuil():\n", " n = 0\n", " u = 27500\n", " while u <= 33000:\n", " n = n + 1\n", " u = 1.04 * u - 156\n", " return n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Capacité 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Question 1 a) : $a_{2} \\approx 14400$ et $a_{8} \\approx 17200$\n", "* Question 1 b) : Le montant de l'APA en 2013 était de $a_{7} = 16744$\n", "* Question 2) a) : $a_{10} = a_{9} \\times 1,05 = 18070 \\times 1,05 = 18973,5$\n", "* Question 2) b) : [feuille de calcul en ligne](https://lite.framacalc.org/9el4-premiereg5-lyceeparc-suites-capacite2)\n", "\n", "
\n", " | \n", " | \n", " | \n", " | \n", " | \n", " | |
n | \n", "9 | \n", "10 | \n", "11 | \n", "12 | \n", "13 | \n", "14 |
a(n) | \n", "18070 | \n", "18973.5 | \n", "19922.175 | \n", "20918.28375 | \n", "21964.1979375 | \n", "23062.407834375 |