JEE Main 2022MathematicsSequences and SeriesMediumNumerical

JEE Main 2022 — Sequences and Series Question with Solution

JEE Main 2022 (29 Jul Shift 1)

Question

Let a1,a2,a3,… be an A.P. If ∑r=1∞ar2r=4, then 4a2 is equal to ______.

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Show full solutionCorrect answer: 16
Correct answer
16

Step-by-step explanation

Let S=∑r=1∞ar2r

⇒S=a12+a222+a323+…  ......1 

⇒S2=  a122+a223+…  .....2

Now subtracting both equation we get, 

⇒S2=a12+d122+123+…

⇒S2=a12+d141-12

⇒S=a1+d=a2

Now given S=∑r=1∞ar2r=4

So, S=a2=4

So, 4a2=16

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About this question

This is a previous-year question from JEE Main 2022, 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.