JEE Main 2021MathematicsSequences and SeriesMediumNumerical

JEE Main 2021 — Sequences and Series Question with Solution

JEE Main 2021 (24 Feb Shift 2)

Question

The sum of first four terms of a geometric progression G.P. is 6512 and the sum of their respective reciprocals is 6518. If the product of first three terms of the G.P. is 1, and the third term is α, then 2α is _________.

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Show full solutionCorrect answer: 3
Correct answer
3

Step-by-step explanation

Let number are a,ar,ar2,ar3

ar4-1r-1=6512 …1

1a1r4-11r-1=6518

1ar31-r41-r=6518 …2

12⇒a2r3=32

and a3·r3=1

ar=1

ar2·r=32

r=32,a=23

So, third term=ar2=23×94

α=32

2α=3

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About this question

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.