Quiz — série28_enreg _tri_arith.pdf

Question 1 sur 10 20:00

[{"id":57797,"question":"Quelle est la formule de la somme des n premiers termes d'une suite arithmétique ?","option_a":"S = n * (a1 + an)","option_b":"S = n\/2 * (a1 + an)","option_c":"S = n * (2a1 + (n-1)r)","option_d":"S = n\/2 * (2a1 + (n-1)r)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule correcte est S = n\/2 * (a1 + an), où a1 est le premier terme et an le dernier terme. Cette formule est équivalente à S = n\/2 * (2a1 + (n-1)r).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"S = n * (a1 + an)\", \"b\": \"S = n\/2 * (a1 + an)\", \"c\": \"S = n * (2a","_debug_options_count":4},{"id":57798,"question":"Si une suite arithmétique a pour premier terme 5 et une raison de 3, quel est son 4ème terme ?","option_a":"11","option_b":"14","option_c":"17","option_d":"20","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le 4ème terme se calcule par an = a1 + (n-1)r. Ici, a4 = 5 + (4-1)*3 = 5 + 9 = 14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"11\", \"b\": \"14\", \"c\": \"17\", \"d\": \"20\"}}","_debug_options_count":4},{"id":57799,"question":"Une suite arithmétique peut avoir une raison négative.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai. La raison d'une suite arithmétique peut être positive, négative ou nulle. Une raison négative signifie que les termes de la suite diminuent.","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":57800,"question":"Quelle est la raison d'une suite arithmétique dont les termes sont 2, 5, 8, 11, ... ?","option_a":"2","option_b":"3","option_c":"5","option_d":"8","option_e":"","option_f":"","bonne_reponse":"b","explication":"La raison se calcule par la différence entre deux termes consécutifs : 5 - 2 = 3. Tous les termes suivent cette progression.","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\": \"3\", \"c\": \"5\", \"d\": \"8\"}}","_debug_options_count":4},{"id":57801,"question":"Si la somme des 10 premiers termes d'une suite arithmétique est 150 et que le premier terme est 5, quelle est la raison ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"On utilise la formule S = n\/2 * (2a1 + (n-1)r). Ici, 150 = 10\/2 * (2*5 + 9r) → 150 = 5*(10 + 9r) → 30 = 10 + 9r → 9r = 20 → r ≈ 2,22 (arrondi à 2 pour simplifier).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\", \"b\": \"2\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":57802,"question":"Toute suite arithmétique est croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux. Une suite arithmétique est croissante si sa raison est positive, décroissante si sa raison est négative, et constante si sa raison est nulle.","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":57803,"question":"Quel est le 7ème terme d'une suite arithmétique où a1 = -2 et r = 4 ?","option_a":"22","option_b":"24","option_c":"26","option_d":"28","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le 7ème terme se calcule par an = a1 + (n-1)r. Ici, a7 = -2 + (7-1)*4 = -2 + 24 = 22.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"22\", \"b\": \"24\", \"c\": \"26\", \"d\": \"28\"}}","_debug_options_count":4},{"id":57804,"question":"Si une suite arithmétique a pour premier terme 10 et une raison de -2, quel est son 5ème terme ?","option_a":"2","option_b":"4","option_c":"6","option_d":"8","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le 5ème terme se calcule par an = a1 + (n-1)r. Ici, a5 = 10 + (5-1)*(-2) = 10 - 8 = 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\": \"4\", \"c\": \"6\", \"d\": \"8\"}}","_debug_options_count":4},{"id":57805,"question":"La formule de la somme des n premiers termes d'une suite arithmétique peut s'écrire S = n * (a1 + an)\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai. Cette formule est une autre écriture de S = n\/2 * (a1 + an), où a1 est le premier terme et an le dernier terme.","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":57806,"question":"Dans une suite arithmétique, la différence entre deux termes consécutifs est toujours la même.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai. Par définition, une suite arithmétique est une suite où la différence entre deux termes consécutifs est constante (cette différence est la raison r).","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}]