st","extracted_subject":"MATH","extracted_chapter":"PROGRESSIONS","extracted_topic":"ARITHMETIC PROGRESSION","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1941.png?top_left_x=1064&top_left_y=1612&width=532&height=259&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31eb3e","slug":"if-a-m-between-psupthsup-and-qsupthsup-terms-of-an","content":"If A. M. between p^th and q^th terms of an A.P. be equal to the A.M. between r^th and s^th terms of the A.P. then p + q is equal to –","options":[{"_id":"68a972697f15af4716d5f5cf","text":"r + s","sequence":0,"isCorrect":true},{"_id":"68a972697f15af4716d5f5d0","text":"\\(\\frac{r - s}{r + s}\\)","sequence":1,"isCorrect":false},{"_id":"68a972697f15af4716d5f5d1","text":"\\(\\frac{r + s}{r - s}\\)","sequence":2,"isCorrect":false},{"_id":"68a972697f15af4716d5f5d2","text":"r + s + 1","sequence":3,"isCorrect":false}],"correct_answer":"r + s","explanation":"If 'a' be first term and 'd' be common difference of the given A.P.\n\nA.M. between a_p and a_q = A.M. between a_r and a_s\n\ñ \\(\\frac{1}{2}\\) (a_p + a_q) = \\(\\frac{1}{2}\\) (a_r + a_s)\n\ñ (p + q – 2) d = (r + s – 2) d\n\ñ p + q = r + s","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.026Z","__v":0,"vector_store_id":"a5b74aab-2384-42f8-beb0-fc2879a6d435","updated_at":"2024-08-30T21:49:38.026Z","isStarred":false},"params":{"questionSlug":"if-a-m-between-psupthsup-and-qsupthsup-terms-of-an"}}]}]]

Question: If A. M. between p<sup>th</sup> and q<sup>th</sup> terms of an A.P. be equal to the A.M. between r<s...

Solution