JEE Main 2021 — Sequences And Series Question with Solution
From: JEE Main 2021 (Online) 18th March Evening Shift
Question
Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :
Choose an option
Show full solutionCorrect option: C
Correct answer
C3000
Step-by-step explanation
S1 = [2a + (2n 1)d]
S2 = [2a + (4n 1)d]
(where a = T1 and d is common difference)
S2 S1 2n[2a + (4n 1)d] n[2a + (2n 1)d] = 1000
n[2a + d(8n 2 2n + 1)] = 1000
n[2a + (6n 1)d] = 1000
S6 = [2a + (6n 1)d] = 3(S2 S1) = 3000
S2 = [2a + (4n 1)d]
(where a = T1 and d is common difference)
S2 S1 2n[2a + (4n 1)d] n[2a + (2n 1)d] = 1000
n[2a + d(8n 2 2n + 1)] = 1000
n[2a + (6n 1)d] = 1000
S6 = [2a + (6n 1)d] = 3(S2 S1) = 3000
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This is a previous-year question from JEE Main 2021, covering the Sequences And Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.