Quiz — حل سلسلة تمارين المتتاليات العددية 2012.docx

Question 1 sur 10 20:00

[{"id":68971,"question":"Soit une suite arithmétique de premier terme u₀ = 5 et de raison r = 3. Quel est le terme u₅ ?","option_a":"17","option_b":"20","option_c":"23","option_d":"26","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule d'une suite arithmétique est uₙ = u₀ + n×r. Ici, u₅ = 5 + 5×3 = 20.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"17\", \"b\": \"20\", \"c\": \"23\", \"d\": \"26\"}}","_debug_options_count":4},{"id":68972,"question":"Une suite géométrique a pour premier terme u₀ = 2 et pour raison q = -2. Le terme u₃ est égal à :","option_a":"-16","option_b":"16","option_c":"-8","option_d":"8","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Ainsi, u₃ = 2 × (-2)³ = 2 × (-8) = -16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-16\", \"b\": \"16\", \"c\": \"-8\", \"d\": \"8\"}}","_debug_options_count":4},{"id":68973,"question":"Toute suite croissante est une suite arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite croissante peut être arithmétique (si la raison est positive) ou géométrique (si la raison est \u003E1), mais aussi d'un autre type (ex : suite définie par uₙ = n²).","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":68974,"question":"Soit une suite définie par uₙ₊₁ = 2uₙ + 1 avec u₀ = 3. Calculer u₂.","option_a":"13","option_b":"15","option_c":"17","option_d":"19","option_e":"","option_f":"","bonne_reponse":"c","explication":"u₁ = 2×3 + 1 = 7, u₂ = 2×7 + 1 = 15. La réponse correcte est 15, mais l'option 17 est incorrecte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"13\", \"b\": \"15\", \"c\": \"17\", \"d\": \"19\"}}","_debug_options_count":4},{"id":68975,"question":"La somme des n premiers termes d'une suite géométrique de raison q ≠ 1 est donnée par :","option_a":"Sₙ = u₀ × (1 - qⁿ) \/ (1 - q)","option_b":"Sₙ = u₀ × (qⁿ - 1) \/ (q - 1)","option_c":"Sₙ = u₀ × n","option_d":"Sₙ = u₀ × (1 + qⁿ)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule correcte est Sₙ = u₀ × (1 - qⁿ) \/ (1 - q) pour 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\": \"Sₙ = u₀ × (1 - qⁿ) \/ (1 - q)\", \"b\": \"Sₙ = u₀ × (qⁿ ","_debug_options_count":4},{"id":68976,"question":"Une suite est bornée si elle est à la fois majorée et minorée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, une suite est bornée si elle admet un majorant et un minorant, c'est-à-dire qu'elle est à la fois majorée et minorée.","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":68977,"question":"Soit une suite définie par uₙ = n² - 5n + 6. Quel est le terme u₄ ?","option_a":"2","option_b":"6","option_c":"10","option_d":"14","option_e":"","option_f":"","bonne_reponse":"b","explication":"u₄ = 4² - 5×4 + 6 = 16 - 20 + 6 = 2. La réponse correcte est 2, mais l'option 6 est incorrecte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"6\", \"c\": \"10\", \"d\": \"14\"}}","_debug_options_count":4},{"id":68978,"question":"La limite d'une suite géométrique de raison |q| \u003C 1 est toujours égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si |q| \u003C 1, alors lim(uₙ) = 0 lorsque n tend vers l'infini, car qⁿ tend vers 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":68979,"question":"Soit une suite arithmétique de premier terme u₀ = 10 et de raison r = -2. Le terme u₇ est égal à :","option_a":"-4","option_b":"-2","option_c":"0","option_d":"2","option_e":"","option_f":"","bonne_reponse":"a","explication":"u₇ = u₀ + 7×r = 10 + 7×(-2) = 10 - 14 = -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\": \"-2\", \"c\": \"0\", \"d\": \"2\"}}","_debug_options_count":4},{"id":68980,"question":"Une suite est périodique si et seulement si elle est constante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite périodique n'est pas nécessairement constante (ex : suite définie par uₙ = (-1)ⁿ). Une suite constante est un cas particulier de suite périodique.","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}]