st","extracted_subject":"MATH","extracted_chapter":"PROGRESSIONS","extracted_topic":"ARITHMETIC PROGRESSION","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1943.png?top_left_x=532&top_left_y=0&width=532&height=267&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31eb45","slug":"if-ssubnsub-denotes-the-sum-of-n-terms-of-an-ap-th","content":"If S_n denotes the sum of n terms of an A.P., then S_n+3 –\n\n3S_n+2 + 3S_n+1 – S_n =","options":[{"_id":"68aa84037f15af4716d9b74d","text":"0","sequence":0,"isCorrect":true},{"_id":"68aa84037f15af4716d9b74e","text":"l","sequence":1,"isCorrect":false},{"_id":"68aa84037f15af4716d9b74f","text":"\\(\\frac{1}{2}\\)","sequence":2,"isCorrect":false},{"_id":"68aa84037f15af4716d9b750","text":"2","sequence":3,"isCorrect":false}],"correct_answer":"0","explanation":"S_n+3 – 3S_n+2 – 3S_n+1 – S_n\n\n= (S_n+3 – S_n+2) –2(S_n+2 – S_n–1) + (S_n+1 – S_n)\n\n= T_n+3 – 2T_n+2 + T_n+1\n\n= (T_n+3 – T_n+2) – (T_n+2 – T_n+1)\n\n= d – d = 0.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.027Z","__v":0,"vector_store_id":"6bf7c057-1f5d-461c-8dc0-fc2c57198991","updated_at":"2024-08-30T21:49:38.027Z","isStarred":false},"params":{"questionSlug":"if-ssubnsub-denotes-the-sum-of-n-terms-of-an-ap-th"}}]}]]

Question: If S<sub>n</sub> denotes the sum of n terms of an A.P., then S<sub>n+3</sub> – 3S<sub>n+2</sub> + 3...

Solution