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Analyse}] + Ci-dessous, vous trouverez 2 début de suites de nombre. + \begin{enumerate} + \item Identifier la nature des suites $(u_n)$ et $(v_n)$ + \item Calculer les 3 termes qui suivent, le 10e terme, le 100e et le 1000e terme. + \item Donner une formule générale pour calculer le n-ième terme d'une suite arithmétique. + \item Donner une formule générale pour calculer le n-ième terme d'une suite géométrique. + \end{enumerate} \end{exercise} -\begin{solution} - <++> -\end{solution} +\begin{exercise}[subtitle={Placement banquaire}, step={1}, origin={??}, topics={Formalisation des suites}, tags={Suites, Analyse}] + On veut placer sur un compte en banque 1000\euro. Le banquier propose deux solutions. -\collectexercisesstop{banque} \ No newline at end of file + \begin{enumerate} + \item Placement à rendement fixe: La valeur du compte en banque augmente de 5\% du placement initiale chaque année. + \item Placement avec intérêt composés: la valeur du compte en banque augmente de 3\% chaque année. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Dépréciation d'un véhicule}, step={1}, origin={??}, topics={Formalisation des suites}, tags={Suites, Analyse}] + Un transporteur a acheté en 2006 un véhicule fourgon de 9 tonnes au prix de \np{50200}\euro, taxes comprises. Compte tenu du nombre de kilomètres parcourus, le véhicule a perdu 20\% de sa valeur chaque année. + + \begin{enumerate} + \item Calculer la valeur du véhicule après 1an puis après 3 ans. + \item Pour tout entier $n$, on note $u_n$, la valeur résiduelle du véhicule l'année "2006+n". + \begin{enumerate} + \item Calculer $u_2$. Interpréter le résultat. + \item Écrire une formule qui modélise le passage de $u_n$ à $u_{n+1}$. + \item En déduire la nature et les paramètres de la suite $(u_n)$. + \item Écrire une formule qui calcule $(u_n)$ pour n'importe quelle valeur de $n$. + \end{enumerate} + \item Calculer la valeur résiduelle du véhicule en 2012. Puis en 2050. Arrondir à l'euro. + \item Écrire un programme Python qui calcul la valeur du véhicule en 2100. + \end{enumerate} +\end{exercise} + + +\collectexercisesstop{banque}