st","extracted_subject":"MATH","extracted_chapter":"BINOMIAL THEOREM AND MATHEMATICAL INDUCTION","extracted_topic":"BINOMIAL THEOREM FOR ANY INDEX","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1989.png?top_left_x=0&top_left_y=1704&width=532&height=246&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f2d0","slug":"if-the-coefficients-of-2supndsup-3suprdsup-and-4su","content":"If the coefficients of 2^nd, 3^rd and 4^th terms in the expansion of (1 + x)²ⁿ are in A.P., then 2n² – 9n + 8 =","options":[{"_id":"68a3d0dd7f15af4716c48618","text":"0","sequence":0,"isCorrect":false},{"_id":"68a3d0dd7f15af4716c48619","text":"1","sequence":1,"isCorrect":true},{"_id":"68a3d0dd7f15af4716c4861a","text":"– 1","sequence":2,"isCorrect":false},{"_id":"68a3d0dd7f15af4716c4861b","text":"None","sequence":3,"isCorrect":false}],"correct_answer":"1","explanation":"We know that is r^th (r + 1)^th (r + 2)^th term coefficient are in an A.P. then m² – (4r + 1) m + 4r² – 2 = 0 then for 2^nd 3^rd , 4^th term r = 2, m = 2n\n\n(2n)² – 9 × 2n + 14 = 0\n\n2n² – 9n + 7 = 0\n\n2n² – 9n + 8 = 1","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.510Z","__v":0,"vector_store_id":"dbdea08b-60e3-45c8-8214-758630379e1c","updated_at":"2024-08-30T21:49:38.510Z","isStarred":false},"params":{"questionSlug":"if-the-coefficients-of-2supndsup-3suprdsup-and-4su"}}]}]]

Question: If the coefficients of 2<sup>nd</sup>, 3<sup>rd</sup> and 4<sup>th</sup> terms in the expansion of (...

Solution