Quiz — Exercice suites extrait du devoir de controle 2015.pdf

Question 1 sur 10 20:00

[{"id":22919,"question":"Quelle est la formule du terme général d'une suite arithmétique de premier terme U_0 et de raison r ?","option_a":"U_n = U_0 + n*r","option_b":"U_n = U_0 * r^n","option_c":"U_n = U_0 + r","option_d":"U_n = n*r","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule correcte est U_n = U_0 + n*r, où n est le rang du terme et r la raison de la suite arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"U_n = U_0 + n*r\", \"b\": \"U_n = U_0 * r^n\", \"c\": \"U_n = U_0 + r\", \"","_debug_options_count":4},{"id":22920,"question":"Une suite géométrique de raison 2 et de premier terme 3 a pour terme général U_n = 3 * 2^n.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule est correcte : U_n = 3 * 2^n pour une suite géométrique de raison 2 et de premier terme 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":22921,"question":"Quelle est la raison d'une suite arithmétique dont les termes sont : 5, 9, 13, 17 ?","option_a":"4","option_b":"3","option_c":"2","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La raison est la différence entre deux termes consécutifs : 9 - 5 = 4, donc la raison est 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"4\", \"b\": \"3\", \"c\": \"2\", \"d\": \"5\"}}","_debug_options_count":4},{"id":22922,"question":"La somme des n premiers termes d'une suite géométrique de raison q ≠ 1 est donnée par S_n = U_0 * (1 - q^n) \/ (1 - q).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule est correcte pour calculer la somme des n premiers termes d'une suite géométrique de raison q ≠ 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":22923,"question":"Quel est le 5ème terme d'une suite arithmétique de premier terme 2 et de raison 3 ?","option_a":"14","option_b":"17","option_c":"11","option_d":"20","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le 5ème terme est U_4 = U_0 + 4*r = 2 + 4*3 = 14 (le premier terme est U_0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"14\", \"b\": \"17\", \"c\": \"11\", \"d\": \"20\"}}","_debug_options_count":4},{"id":22924,"question":"Une suite est définie par U_{n+1} = 2*U_n + 1. Peut-on affirmer qu'elle est géométrique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique a une relation de la forme U_{n+1} = q*U_n. Ici, la relation n'est pas de cette forme, donc la suite n'est pas géométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":22925,"question":"Quelle est la raison d'une suite géométrique dont les termes sont : 2, 6, 18, 54 ?","option_a":"3","option_b":"2","option_c":"4","option_d":"6","option_e":"","option_f":"","bonne_reponse":"a","explication":"La raison est le rapport entre deux termes consécutifs : 6 \/ 2 = 3, donc la raison est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\", \"b\": \"2\", \"c\": \"4\", \"d\": \"6\"}}","_debug_options_count":4},{"id":22926,"question":"La suite définie par U_n = 5 - 2n est une suite arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite U_n = 5 - 2n est de la forme U_n = U_0 + n*r avec U_0 = 5 et r = -2, donc c'est une suite arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":22927,"question":"Quel est le terme général d'une suite géométrique de premier terme 4 et de raison 1\/2 ?","option_a":"U_n = 4 * (1\/2)^n","option_b":"U_n = 4 + n*(1\/2)","option_c":"U_n = 4 * 2^n","option_d":"U_n = 4 \/ n","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général d'une suite géométrique est U_n = U_0 * q^n, donc ici U_n = 4 * (1\/2)^n.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"U_n = 4 * (1\/2)^n\", \"b\": \"U_n = 4 + n*(1\/2)\", \"c\": \"U_n = 4 * 2^n","_debug_options_count":4},{"id":22928,"question":"La suite définie par U_0 = 1 et U_{n+1} = U_n + 3 est une suite arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite est définie par une relation de récurrence de la forme U_{n+1} = U_n + r, donc c'est une suite arithmétique de raison 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]