Quiz — 66cb6ea31aa7d__Correction série1-suite 25-08-24.pdf

Question 1 sur 5 10:00

[{"id":244,"question":"Quelle est la formule explicite d'une suite géométrique de premier terme u₀ et de raison r ?","option_a":"uₙ = u₀ + n × r","option_b":"uₙ = u₀ × rⁿ","option_c":"uₙ = u₀ + rⁿ","option_d":"uₙ = u₀ × (1 + r)ⁿ","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule explicite d'une suite géométrique est uₙ = u₀ × rⁿ, où u₀ est le premier terme et r la raison. Cette formule permet de calculer directement n'importe quel terme de la suite sans avoir à calculer tous les termes précédents.","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 × r\", \"b\": \"uₙ = u₀ × rⁿ\", \"c\": \"uₙ = u","_debug_options_count":4},{"id":245,"question":"Soit une suite arithmétique de premier terme u₁ = 5 et de raison r = 3. Quel est le terme u₁₀ ?","option_a":"32","option_b":"35","option_c":"29","option_d":"38","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une suite arithmétique, le terme uₙ = u₁ + (n-1) × r. Ici, u₁₀ = 5 + (10-1) × 3 = 5 + 27 = 32.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"32\", \"b\": \"35\", \"c\": \"29\", \"d\": \"38\"}}","_debug_options_count":4},{"id":246,"question":"Quelle est la somme des 10 premiers termes d'une suite arithmétique de premier terme u₁ = 2 et de raison r = 4 ?","option_a":"200","option_b":"220","option_c":"190","option_d":"210","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des n premiers termes d'une suite arithmétique est donnée par Sₙ = n\/2 × (2u₁ + (n-1)r). Ici, S₁₀ = 10\/2 × (2×2 + 9×4) = 5 × (4 + 36) = 5 × 40 = 200.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"200\", \"b\": \"220\", \"c\": \"190\", \"d\": \"210\"}}","_debug_options_count":4},{"id":247,"question":"Soit une suite définie par uₙ₊₁ = 2uₙ + 1 avec u₀ = 3. Quel est le terme u₃ ?","option_a":"23","option_b":"15","option_c":"29","option_d":"31","option_e":"","option_f":"","bonne_reponse":"d","explication":"Calculons les termes pas à pas : u₁ = 2×3 + 1 = 7, u₂ = 2×7 + 1 = 15, u₃ = 2×15 + 1 = 31.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"23\", \"b\": \"15\", \"c\": \"29\", \"d\": \"31\"}}","_debug_options_count":4},{"id":248,"question":"Quelle est la limite d'une suite géométrique de raison r = 0.5 ?","option_a":"La suite diverge vers +∞","option_b":"La suite converge vers 0","option_c":"La suite converge vers 1","option_d":"La suite oscille indéfiniment","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique de raison |r| \u003C 1 converge vers 0. Ici, r = 0.5, donc la suite converge vers 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\": \"La suite diverge vers +∞\", \"b\": \"La suite converge vers 0\", \"c\"","_debug_options_count":4}]