{"id":5271,"date":"2019-01-30T09:19:11","date_gmt":"2019-01-30T08:19:11","guid":{"rendered":"http:\/\/mathsguyon.fr\/?page_id=5271"},"modified":"2020-12-13T21:47:59","modified_gmt":"2020-12-13T20:47:59","slug":"les-suites-arithmetico-geometriques","status":"publish","type":"page","link":"https:\/\/mathsguyon.fr\/?page_id=5271","title":{"rendered":"Les suites arithm\u00e9tico-g\u00e9om\u00e9triques"},"content":{"rendered":"\r\n

Exercices fondamentaux corrig\u00e9s en vid\u00e9o <\/strong><\/p>\r\n\r\n\r\n\r\n

D\u00e9duire une suite g\u00e9om\u00e9trique d’une suite arithm\u00e9tico-g\u00e9om\u00e9trique<\/strong><\/p>\r\n\r\n\r\n\r\n

Pour tout entier naturel $n$, on a $a_{n+1}=1,02 ~a_n – 100$.<\/p>\r\n\r\n\r\n\r\n

On donne $a_0=2000$<\/p>\r\n\r\n\r\n\r\n

On consid\u00e8re la suite$(b_n)$ d\u00e9finie pour tout nombre entier naturel $n$par $b_n=a_n-5000$.<\/p>\r\n\r\n\r\n\r\n

D\u00e9montrer que la suite$(b_n)$ est g\u00e9om\u00e9trique. Pr\u00e9ciser son premier terme $b_0$ et sa raison.<\/p>\r\n\r\n\r\n\r\n

Correction en vid\u00e9o<\/a><\/p>\r\n\r\n\r\n\r\n

D\u00e9terminer le terme g\u00e9n\u00e9ral d’une suite arithm\u00e9tico-g\u00e9om\u00e9triques<\/strong><\/p>\r\n\r\n\r\n\r\n

A la question pr\u00e9c\u00e9dente, on a montr\u00e9 que $b_{n+1}=1,02 ~b_n $ et $b=-3000$.<\/p>\r\n\r\n\r\n\r\n

En d\u00e9duire $a_n$ en fonction de $n$<\/p>\r\n\r\n\r\n\r\n

Correction<\/a><\/p>\r\n\r\n\r\n\r\n

D\u00e9terminer la limite d’une suite arithm\u00e9tico-g\u00e9ometriques<\/strong><\/p>\r\n\r\n\r\n\r\n

D\u00e9terminer la limite de la suite $a_n = {5000} – {3000} \\times 1,02^n$.<\/p>\r\n\r\n\r\n\r\n

Correction<\/a><\/p>\r\n\r\n\r\n\r\n

Compl\u00e9ter un algorithme \u00e0 partir d’une suite arithm\u00e9tico-g\u00e9om\u00e9triques<\/strong><\/p>\r\n\r\n\r\n\r\n

Recopier et compl\u00e9ter l’algorithme suivant afin qu’il d\u00e9termine le plus petit entier $n$ tel que $a_n \\leq 0$ :<\/p>\r\n\r\n\r\n\r\n

\"\"<\/figure>\r\n\r\n\r\n\r\n

Correction<\/a><\/p>\r\n\r\n\r\n\r\n

R\u00e9soudre une in\u00e9quation avec l’inconnue en exposant :<\/strong><\/p>\r\n\r\n\r\n\r\n

R\u00e9soudre par le calcul l’in\u00e9quation $5000 – 3000 \\times 1,02^n \\leqslant 0$.<\/p>\r\n\r\n\r\n\r\n

 <\/p>\r\n","protected":false},"excerpt":{"rendered":"

Exercices fondamentaux corrig\u00e9s en vid\u00e9o D\u00e9duire une suite g\u00e9om\u00e9trique d’une suite arithm\u00e9tico-g\u00e9om\u00e9trique Pour tout entier naturel $n$, on a $a_{n+1}=1,02 ~a_n – 100$. On donne $a_0=2000$ On consid\u00e8re la suite$(b_n)$ d\u00e9finie pour tout nombre entier naturel $n$par $b_n=a_n-5000$. D\u00e9montrer que … Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5271","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5271","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5271"}],"version-history":[{"count":44,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5271\/revisions"}],"predecessor-version":[{"id":8017,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5271\/revisions\/8017"}],"wp:attachment":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}