Quiz — Suites arithmétiques ou géométriques.pdf

Question 1 sur 10 20:00

[{"id":22339,"question":"Quelle est la formule du terme général d'une suite arithmétique 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 = u_1 * (1 - r^n) \/ (1 - r)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule correcte est u_n = u_0 + n * r, où u_0 est le premier terme et r la raison.","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":22340,"question":"Une suite géométrique peut-elle avoir une raison nulle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Non, car si q = 0, tous les termes après le premier sont nuls, ce qui n'est pas une suite géométrique classique.","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":22341,"question":"Quel est le terme général d'une suite géométrique de premier terme u_1 = 5 et de raison q = 2 ?","option_a":"u_n = 5 * 2^(n-1)","option_b":"u_n = 5 + 2n","option_c":"u_n = 5 * n^2","option_d":"u_n = 2 * 5^n","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général est u_n = u_1 * q^(n-1) = 5 * 2^(n-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\": \"u_n = 5 * 2^(n-1)\", \"b\": \"u_n = 5 + 2n\", \"c\": \"u_n = 5 * n^2\", \"d","_debug_options_count":4},{"id":22342,"question":"La somme des n premiers termes d'une suite arithmétique est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux, car si la raison est négative et les termes initiaux petits, la somme peut être négative.","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":22343,"question":"Quelle est la raison d'une suite arithmétique dont les termes u_2 = 7 et u_5 = 16 ?","option_a":"3","option_b":"2","option_c":"4","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La raison r = (u_5 - u_2) \/ (5 - 2) = (16 - 7) \/ 3 = 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\": \"1\"}}","_debug_options_count":4},{"id":22344,"question":"La suite définie par u_n = 3 * (-1)^n est-elle géométrique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car chaque terme est obtenu en multipliant le précédent par -1 (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":22345,"question":"Quel est le premier terme d'une suite géométrique de raison 2 et de somme des 3 premiers termes égale à 35 ?","option_a":"5","option_b":"7","option_c":"10","option_d":"14","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme S = u_1 * (1 - q^3) \/ (1 - q) = 35 donne u_1 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5\", \"b\": \"7\", \"c\": \"10\", \"d\": \"14\"}}","_debug_options_count":4},{"id":22346,"question":"Une suite arithmétique de raison 0 est-elle constante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car tous les termes sont égaux à u_0.","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":22347,"question":"Quelle formule permet de calculer la somme des n premiers termes d'une suite arithmétique ?","option_a":"S = n * (u_1 + u_n) \/ 2","option_b":"S = u_1 * (1 - q^n) \/ (1 - q)","option_c":"S = n * u_1 + n(n-1)r\/2","option_d":"S = u_1 + u_2 + ... + u_n","option_e":"","option_f":"","bonne_reponse":"c","explication":"La formule correcte est S = n * u_1 + n(n-1)r\/2 ou S = n * (u_1 + u_n) \/ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"S = n * (u_1 + u_n) \/ 2\", \"b\": \"S = u_1 * (1 - q^n) \/ (1 - q)\", \"","_debug_options_count":4},{"id":22348,"question":"Si u_3 = 12 et u_6 = 96 dans une suite géométrique, quelle est la raison q ?","option_a":"2","option_b":"3","option_c":"4","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"On a u_6 = u_3 * q^(6-3) =\u003E 96 = 12 * q^3 =\u003E q^3 = 8 =\u003E q = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2\", \"b\": \"3\", \"c\": \"4\", \"d\": \"1\/2\"}}","_debug_options_count":4}]