Quiz — Série N°6_(Suites).pdf

Question 1 sur 5 10:00

[{"id":1608,"question":"Quelle est la formule explicite d'une suite arithmétique de premier terme u₀ et de raison r ?","option_a":"uₙ = u₀ + n","option_b":"uₙ = u₀ + n·r","option_c":"uₙ = u₀·rⁿ","option_d":"uₙ = u₀ + rⁿ","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule explicite d'une suite arithmétique est uₙ = u₀ + n·r, où u₀ est le premier terme et r la raison constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"uₙ = u₀ + n\", \"b\": \"uₙ = u₀ + n·r\", \"c\": \"uₙ = u₀·r","_debug_options_count":4},{"id":1609,"question":"Soit une suite géométrique de raison q = -2 et de premier terme u₀ = 3. Quelle est la valeur de u₃ ?","option_a":"-24","option_b":"12","option_c":"-12","option_d":"24","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une suite géométrique, uₙ = u₀·qⁿ. Donc u₃ = 3·(-2)³ = 3·(-8) = -24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-24\", \"b\": \"12\", \"c\": \"-12\", \"d\": \"24\"}}","_debug_options_count":4},{"id":1610,"question":"Quelle propriété caractérise une suite géométrique ?","option_a":"La différence entre deux termes consécutifs est constante","option_b":"Le rapport entre deux termes consécutifs est constant","option_c":"La somme de deux termes consécutifs est constante","option_d":"Le produit de deux termes consécutifs est constant","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique est définie par un rapport constant entre deux termes consécutifs, appelé raison q.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"La différence entre deux termes consécutifs est constante\", \"b\"","_debug_options_count":4},{"id":1611,"question":"Soit la suite définie par uₙ₊₁ = 2uₙ + 1 avec u₀ = 0. Que vaut u₂ ?","option_a":"3","option_b":"5","option_c":"7","option_d":"9","option_e":"","option_f":"","bonne_reponse":"c","explication":"Calculons les termes : u₁ = 2·0 + 1 = 1, u₂ = 2·1 + 1 = 3. Attention, u₂ = 3, pas 7. Correction : u₂ = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"3\", \"b\": \"5\", \"c\": \"7\", \"d\": \"9\"}}","_debug_options_count":4},{"id":1612,"question":"Quelle est la limite de la suite uₙ = (3n² + 2n - 1)\/(5n² - n + 4) quand n tend vers l'infini ?","option_a":"0","option_b":"3\/5","option_c":"1","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour les suites rationnelles, on compare les termes de plus haut degré : uₙ ≈ 3n²\/5n² = 3\/5. La limite est donc 3\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"3\/5\", \"c\": \"1\", \"d\": \"+∞\"}}","_debug_options_count":4}]