On considère les deux suites un et vn définies par :[br][math]u_0=1[/math] ; [math]v_0=7[/math] ; [math]u_{n+1}=\frac{2u_n+v_n}{3}[/math] ; [math]v_{n+1}=\frac{u_n+2v_n}{3}[/math][br]Ces deux suites sont adjacentes : leur représentation dans le plan permettra de mettre en[br]évidence cette propriété.[br]1. Afficher le panneau “Tableur” en actionnant la commande suivante via la barre des menus :[br]Affichage -> Tableur[br][br]2. Saisir les commandes suivantes :[br]a. A1=0 b. A2=A1+1 c. B1=1 d. B2=1/3*(2*B1+C1) e. C1=7 f. C2=1/3*(B1+2*C1)[br][br]3. Sélectionner la plage A2:C2 et étirer cette plage jusqu’à la ligne 20.[br]4. a. Sélectionner la plage A1:B20, puis créer les points correspondants à l’aide du bouton 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wm9lA+r5QAfFVTWQPocgKHBhlLC6Kpx0iIrMDmELUAc78d9cNaNoK5IxpMfJFttYsjJ2l+H0nBiaYb1e71scGYpjfFOYoENcrj/Y5RNKZg1dnLUy3pHJ9m1TZwOsc5bYAeWpEyinXkGuOZSsgNIetUZTDjl4vZ9q+mMqHcZt6JcXAzrcResGYwTh0qUkhlbwNcwy5hIpTLKcwI0wqFObeciMtdcA8KNcL98l5NmujgZgafbDh/MKOXOl9yU8xCZkuqr+HnlBL7Re+S5O/c1FNzNIVyssKNyOxcRUSo/aEP5ziWVlZoy2A6XKTExyn4Gsqb+H1BtQJ2AOoG8T4C/Ccm/1HzZH5juGblm0lIgAAAAAElFTkSuQmCC[/img].[br]b. En utilisant la touche Ctrl, sélectionner conjointement les plages A1:A20 et C1:C20, puis[br]créer la liste de points correspondants .[br]5. Quelle relation semble relier les suites [math]u_n[/math] et [math]v_n[/math]?
[br][u][b]Exercice d'application[/b][/u][br]On considère la fonction f définie sur ] [math]-\infty;\frac{9}{2}[/math] [ par la relation :[br][math]f(x)=\frac{x-8}{2x-9}[/math][br]La suite [math]u_n[/math] est définie par les relations : [math]u_0=3,9[/math] et [math]u_{n+1}=f\left(u_n\right)[/math][br][br]Tracer la courbe représentative de la fonction f et représenté les dix premiers termes de cette[br]suite sur l’axe des abscisses.