Maîtrisez les suites numériques : QCM et Vrai/Faux pour tester vos connaissances

Question 1 sur 10 10:00

[{"id":32208,"question":"Quelle est la formule du terme général d'une suite arithmétique de raison r et de premier terme u₀ ?","option_a":"uₙ = u₀ + n","option_b":"uₙ = u₀ + n*r","option_c":"uₙ = u₀ * rⁿ","option_d":"uₙ = u₀ + r","option_e":"","option_f":"","bonne_reponse":"B","explication":"La formule correcte est uₙ = u₀ + n*r, où n est le rang du terme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32209,"question":"Une suite géométrique de raison 2 et de premier terme 3 est croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite est croissante car la raison (2) est supérieure à 1 et le premier terme (3) est positif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32210,"question":"Quel est le terme général d'une suite géométrique de premier terme 5 et de raison 1\/2 ?","option_a":"uₙ = 5 * (1\/2)ⁿ","option_b":"uₙ = 5 * 2ⁿ","option_c":"uₙ = 5 + n\/2","option_d":"uₙ = 5 * n^(1\/2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule correcte est uₙ = 5 * (1\/2)ⁿ, car la raison est 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32211,"question":"La somme des n premiers termes d'une suite arithmétique est donnée par Sₙ = n(u₁ + uₙ)\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule est correcte : Sₙ = n(u₁ + uₙ)\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32212,"question":"Quelle est la raison d'une suite géométrique dont le 3ème terme est 16 et le 5ème terme est 64 ?","option_a":"2","option_b":"4","option_c":"8","option_d":"16","option_e":"","option_f":"","bonne_reponse":"B","explication":"La raison r vérifie u₅ = u₃ * r² → 64 = 16 * r² → r² = 4 → r = 2 (car la suite est croissante).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32213,"question":"Une suite définie par uₙ₊₁ = 2uₙ + 1 est une suite arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette suite est récurrente linéaire d'ordre 1, mais pas arithmétique car la relation n'est pas de la forme uₙ₊₁ = uₙ + r.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32214,"question":"Quel est le 10ème terme d'une suite arithmétique de premier terme 7 et de raison -3 ?","option_a":"-20","option_b":"-23","option_c":"-26","option_d":"-29","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le 10ème terme est u₉ = u₀ + 9*r = 7 + 9*(-3) = 7 - 27 = -20. Attention à l'indexation (u₀ est le 1er terme).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32215,"question":"La somme des 5 premiers termes d'une suite géométrique de premier terme 1 et de raison 3 est 121.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme est S₅ = (3⁵ - 1)\/(3 - 1) = (243 - 1)\/2 = 121. La réponse est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32216,"question":"Quelle est la limite d'une suite géométrique de raison 0.5 et de premier terme 10 ?","option_a":"0","option_b":"10","option_c":"∞","option_d":"La suite n'a pas de limite","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite est 0 car la raison (0.5) est comprise entre -1 et 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32217,"question":"Une suite définie par uₙ = 2ⁿ est une suite géométrique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite est géométrique de raison 2, car uₙ₊₁ = 2 * uₙ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]