JEE Main 2021 — Sequences And Series Question with Solution
From: JEE Main 2021 (Online) 31st August Morning Shift
Question
Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3 r2, then r2 d is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B7 +
Step-by-step explanation
Let numbers be , a, ar G.P.
, 2a, ar A.P. 4a = + ar r + = 4
r = 2
4th form of G.P. = 3r2 ar2 = 3r2 a = 3
r = 2 + , a = 3, d = 2a = 3
r2 d = (2 + )2 3
= 7 + 4 3
= 7 +
, 2a, ar A.P. 4a = + ar r + = 4
r = 2
4th form of G.P. = 3r2 ar2 = 3r2 a = 3
r = 2 + , a = 3, d = 2a = 3
r2 d = (2 + )2 3
= 7 + 4 3
= 7 +
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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.