JEE Main 2021MathematicsSequences and SeriesHardMCQ

JEE Main 2021 — Sequences and Series Question with Solution

JEE Main 2021 (26 Feb Shift 1)

Question

In an increasing geometric series, the sum of the second and the sixth term is 252 and the product of the third and fifth term is 25. Then, the sum of 4th,6th and 8th terms is equal to:

Choose an option

Show full solutionCorrect option: A
Correct answer
A35

Step-by-step explanation

a, ar, ar2....

T2+T6=252⇒ar1+r4=252

a2r21+r42=6254   ⋯1

T3·T5=25⇒ar2ar4=25

a2r6=25   ...2

On dividing 1 by 2

1+r42r4=254

4r8-17r4+4=0

4r4-1r4-4=0

r4=14,4⇒r4=4 (an increasing geometric series)

a2r6=25⇒ar32=25

T4+T6+T8=ar3+ar5+ar7

=ar31+r2+r4

=51+2+4=35

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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.