JEE Main 2022MathematicsSequences and SeriesMediumNumerical

JEE Main 2022 — Sequences and Series Question with Solution

JEE Main 2022 (29 Jun Shift 2)

Question

Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to ______.

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Show full solutionCorrect answer: 2223
Correct answer
2223

Step-by-step explanation

Given,

3,6,9,⋯ upto 78 terms

⇒t78=3+77×3=234

5,9,13,⋯ upto 59 terms

⇒t59=5+58×4=237

Common difference of common terms =LCM3,4=12

First common term is 9 and last common term is 225

So series will be 9,21,33,⋯,225  ⇒n=19

S=n2a+l=1929+225=2223

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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.