{"id":7230,"date":"2020-05-03T22:09:09","date_gmt":"2020-05-03T21:09:09","guid":{"rendered":"http:\/\/mathsguyon.fr\/?page_id=7230"},"modified":"2024-02-02T07:46:17","modified_gmt":"2024-02-02T06:46:17","slug":"suites-arithmetiques-et-geometriques","status":"publish","type":"page","link":"https:\/\/mathsguyon.fr\/?page_id=7230","title":{"rendered":"suites arithm\u00e9tiques et g\u00e9om\u00e9triques"},"content":{"rendered":"

Cours en pdf<\/a>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Plan de travail<\/a><\/h2>\n
\n

1. D\u00e9finition d’une suite arithm\u00e9tique<\/strong><\/h2>\n

Vid\u00e9o 1<\/a> \u00a0\u00a0\u00a0 – \u00a0\u00a0 \u00a0 QCM 1:<\/strong> Identifi\u00e9\u00a0\u00a0<\/a> –\u00a0\u00a0 Anonyme<\/a><\/h2>\n

Exercice 1 : <\/span><\/strong><\/p>\n

1. La suite \\(( u_n )\\) d\u00e9finie par : \\(u_n = 5 \u2013 7n\\) est-elle arithm\u00e9tique ?\u00a0\u00a0 correction \u00e9crite<\/strong><\/a><\/span>
\n2) La suite \\(( v_n )\\) d\u00e9finie par : \\(v_n = n\u00b2 + 9\\) est-elle arithm\u00e9tique ?\u00a0 correction \u00e9crite<\/strong><\/a><\/span><\/p>\n

\n

2. Terme g\u00e9n\u00e9ral d’une suite arithm\u00e9tique<\/strong><\/h2>\n

Vid\u00e9o 2 <\/a>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 – \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Vid\u00e9o 3 : D\u00e9monstration fondamentale<\/a><\/h2>\n

QCM 2:<\/strong> Identifi\u00e9<\/a>\u00a0\u00a0 –\u00a0\u00a0 Anonyme<\/a><\/h2>\n

Exercice 2 :\u00a0 Correction \u00e9crite<\/a><\/span><\/strong><\/span><\/p>\n

Consid\u00e9rons la suite arithm\u00e9tique\\((u_n\\)) tel que \\({u}_{5}=4\\) et \\({u}_{9}=24\\)
\n1) D\u00e9terminer la raison et le premier terme de la suite \\((u_n\\)).
\n2) Exprimer \\(u_{n}\\) en fonction de \\(n\\)<\/p>\n

Exercice 3 : Correction \u00e9crite<\/span><\/a><\/strong><\/span>
\nSoit \\(( v_n )\\)\u00a0 une suite arithm\u00e9tique ayant comme second terme \\({v}_{1}=5\\) et 9 \u00e8me terme \\(v_{8}=8,5\\)
\nCalculer la raison de la suite \\(( v_n )\\)\u00a0 et son premier terme.<\/p>\n

\n

3. Sens de variation d’une suite arithm\u00e9tique<\/strong><\/h2>\n

Vid\u00e9o 4 <\/a>\u00a0\u00a0 – \u00a0\u00a0 QCM 3:<\/strong> Identifi\u00e9\u00a0\u00a0<\/a> –\u00a0\u00a0 Anonyme<\/a><\/h2>\n

Exercice 4 :<\/span> Correction \u00e9crite<\/span><\/a>
\n<\/strong><\/p>\n

D\u00e9terminer le sens de variation de la suite \\((u_n\\)) d\u00e9finie par \\(u_{n+1} =u_n + 2\\) et \\(u_0 = 11\\).<\/p>\n

Exercice 5 :<\/span> Correction \u00e9crite<\/a><\/span><\/strong><\/p>\n

D\u00e9terminer le sens de variation de la suite \\((u_n\\)) d\u00e9finie par \\(u_{n+1} =u_n -5\\) et \\(u_0 = 7\\).<\/p>\n

\n

4. Somme des termes d’une suite arithm\u00e9tique :<\/strong><\/h2>\n

Vid\u00e9o 5 : D\u00e9monstration fondamentale\u00a0<\/a> – \u00a0 Vid\u00e9o 6 : Le cours<\/a><\/h2>\n

Le cours \u00e0 lire<\/a><\/h2>\n

QCM 4:<\/strong> Identifi\u00e9\u00a0\u00a0<\/a> –\u00a0\u00a0 Anonyme<\/a><\/h2>\n

Exercice 6 :
\n<\/strong><\/span><\/p>\n

1. Calcul de la valeur de \\(S = 1 + 2 + 3 + \u2026 + 133\\)\u00a0\u00a0\u00a0\u00a0Correction \u00e9crite<\/span><\/a>
\n<\/strong><\/p>\n

2. Calcul de la valeur de \\(S = 30 + 33 + 36 + \u2026+ 264\\) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Correction \u00e9crite<\/a><\/span>
\n<\/strong><\/p>\n

Exercice 7 :<\/strong><\/span><\/p>\n

1. On consid\u00e8re la suite \\(( u_n )\\) arithm\u00e9tique de premier terme 3 et de raison 2.<\/p>\n

D\u00e9terminer la valeur de la somme : \\(S = u_0 + u_1 + \u00b7 \u00b7 \u00b7 + u_{34}\\)\u00a0 Correction \u00e9crite<\/a><\/strong><\/span><\/p>\n

2. On consid\u00e8re la suite (\u00a0vn<\/sub>\u00a0)\u00a0d\u00e9finie pour tout entier naturel n (n\u2208N) par :\u00a0vn<\/sub> = 2\u22123n<\/p>\n

D\u00e9terminer la valeur de la somme : \\(S = v_4 + \\dots + v_{15}\\)\u00a0\u00a0\u00a0\u00a0 Correction \u00e9crite<\/a><\/span><\/strong><\/p>\n

3. Une horloge sonne toutes les heures, de 1 coup \u00e0 1 heure du matin \u00e0 24 coups \u00e0 minuit. Quel est le nombre de sons de cloche entendus en 24 heures ? Correction \u00e9crite<\/a><\/span><\/p>\n

4. Soit une suite arithm\u00e9tique \\(( u_n )\\) de raison 5,\u00a0 telle que \\(u_{0}=2\\). \\(n\\) \u00e9tant un nombre entier, on a : \\(\\displaystyle\\sum_{i=3}^{i=n} u_{i}=6456 .\\) Calculez \\(n\\) \u00a0\u00a0 Correction \u00e9crite<\/a><\/span><\/p>\n

Pour aller plus loin (trop loin ??) :<\/strong> <\/span>L’\u00e9galit\u00e9 \\(1 + 2 + 3 + 4 + .. = -\\dfrac{1}{12}\\), est-elle vraie ? \u00a0Vid\u00e9o de<\/a> Benoit Rittaud<\/a><\/p>\n

\n

5. Repr\u00e9sentation graphique d’une suite arithm\u00e9tique<\/strong><\/h2>\n

Vid\u00e9o 7<\/a> \u00a0\u00a0\u00a0\u00a0\u00a0QCM 5: Identifi\u00e9\u00a0\u00a0<\/a> –\u00a0\u00a0 Anonyme<\/a><\/h2>\n
\n

6. D\u00e9finition d’une suite g\u00e9om\u00e9trique<\/strong><\/h2>\n

Vid\u00e9o 8\u00a0<\/a> QCM 6: Identifi\u00e9\u00a0\u00a0<\/a> –\u00a0\u00a0 Anonyme<\/a><\/h2>\n

Exercice 8 : Correction <\/span><\/a>
\n<\/strong><\/span><\/p>\n

Les nombres suivants sont-ils en progression g\u00e9om\u00e9trique ? 346834 ; 3434 ; 34<\/p>\n

Exercice 9 :<\/strong><\/span><\/p>\n

Ces deux suites sont-elles g\u00e9om\u00e9triques ? Correction\u00a0 \\((u_n)\\)<\/a><\/strong>\u00a0 – \u00a0\u00a0 correction \\((v_n)\\)<\/a><\/strong><\/span><\/p>\n

$$\\left\\{\\begin{array}{l}u_{0}&=7 \\\\u_{n+1}&=u_{n}^{2}\\end{array}\\right .$$<\/p>\n

\\[\\left\\{\\begin{array}{l}v_{0}&=100 \\\\ v_{n+1}&=v_{n}+\\frac{6}{100} v_{n}\\end{array}\\right .\\]<\/p>\n

\n

7. \u00c9volution en pourcentage
\n<\/strong><\/h2>\n

Vid\u00e9o 9<\/a> – QCM 7: Identifi\u00e9\u00a0\u00a0<\/a> –\u00a0\u00a0 Anonyme<\/a><\/h2>\n
\n

8. Terme g\u00e9n\u00e9ral d’une suite g\u00e9om\u00e9trique<\/strong><\/h2>\n

Vid\u00e9o 10<\/a> – Vid\u00e9o 11 : D\u00e9monstration fondamentale<\/a><\/h2>\n

QCM 8: Identifi\u00e9\u00a0\u00a0<\/a> –\u00a0\u00a0 Anonyme<\/a><\/h2>\n

Exercice 10 :<\/strong><\/span><\/p>\n

\\(\\left(u_{n}\\right)\\) est une suite g\u00e9om\u00e9trique de raison \\(q\\)
\n1) On sait que \\(u_{0}=32\\) et \\(q=\\dfrac{1}{4} \\). Calculer \\(u_{2}, u_{3}, u_{5}, u_{8}\\)\u00a0 Correction<\/a><\/strong><\/span>
\n2) On sait que \\(u_{1}=\\dfrac{1}{125}\\) et \\(q=5 \\). Calculer \\(u_{0}, u_{5}, u_{7}, u_{20}\\)\u00a0 Correction<\/span><\/strong><\/a>
\n3) On sait que \\(u_{0}=1\\) et \\(u_{1}=\\dfrac{1}{3}\\). Calculer \\(q, u_{2}\\) et \\(u_{5}\\)\u00a0 Correction<\/strong><\/span><\/a>
\n4) On sait que \\(u_{0}=3\\) et \\(u_{2}=12 \\). Calculer \\(q, u_{1}\\) et \\(u_{5}\\)\u00a0\u00a0 Correction<\/a><\/strong><\/span>
\n5) On sait que \\(u_{1}=-1\\) et \\(u_{10}=1\\). Calculer \\(q, u_{0}\\) et \\(u_{5}\\)\u00a0 Correction<\/strong><\/a><\/span><\/p>\n

\n

9. Sens de variation d’une suite g\u00e9om\u00e9trique<\/strong><\/h2>\n

Vid\u00e9o 12\u00a0 <\/a>– Vid\u00e9o 13<\/a> : D\u00e9monstration fondamentale
\n<\/strong><\/h2>\n

QCM 9: Identifi\u00e9\u00a0\u00a0<\/a> –\u00a0\u00a0 Anonyme<\/h2>\n

QCM 10 (Algorithme de seuil) : Identifi\u00e9<\/a><\/h2>\n
\n

10.Somme des termes d’une suite g\u00e9om\u00e9trique
\n<\/strong><\/h2>\n

Vid\u00e9o 14<\/a> : Activit\u00e9\u00a0 – Vid\u00e9o 15<\/a> : \\(Calcul de 1+q+q^2+…+q^n\\) –<\/h2>\n

Vid\u00e9o 16<\/a>: Somme des termes d’une suite g\u00e9om\u00e9trique
\n<\/strong><\/h2>\n

Vid\u00e9o 17<\/a> : D\u00e9monstration fondamentale somme des termes g\u00e9om\u00e9triques<\/h2>\n

\u00a0\u00a0\u00a0\u00a0 QCM 10: Identifi\u00e9\u00a0\u00a0 –\u00a0\u00a0 Anonyme<\/h2>\n
\n

11. Repr\u00e9sentation graphique d’une suite g\u00e9om\u00e9trique<\/strong><\/h2>\n

\u00a0Vid\u00e9o 18<\/a> –\u00a0 QCM 11: Identifi\u00e9\u00a0\u00a0 –\u00a0\u00a0 Anonyme<\/h2>\n","protected":false},"excerpt":{"rendered":"

Cours en pdf\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Plan de travail 1. D\u00e9finition d’une suite arithm\u00e9tique Vid\u00e9o 1 \u00a0\u00a0\u00a0 – \u00a0\u00a0 \u00a0 QCM 1: Identifi\u00e9\u00a0\u00a0 –\u00a0\u00a0 Anonyme Exercice 1 : 1. La suite \\(( u_n )\\) d\u00e9finie par : \\(u_n = 5 \u2013 7n\\) est-elle … 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-7230","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/7230","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=7230"}],"version-history":[{"count":121,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/7230\/revisions"}],"predecessor-version":[{"id":9477,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/7230\/revisions\/9477"}],"wp:attachment":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}