JEE Main 2024MathematicsSequences and SeriesEasyNumerical

JEE Main 2024 — Sequences and Series Question with Solution

JEE Main 2024 (01 Feb Shift 1)

Question

Let 3, 7,11, 15,..,403 and 2, 5, 8, 11,...,404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to_________

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Show full solutionCorrect answer: 6699
Correct answer
6699

Step-by-step explanation

Given AP are: 3, 7,11, 15,..,403 and 2, 5, 8, 11,...,404

a1=3, a2=2, d1=4, d2=3

So, for the common AP,

a=11, d=LCM3,4=12

Also, an≤403

⇒11+n-112≤403

⇒-1+12n≤403

⇒n≤40412

⇒n≤33.6

⇒n=33

⇒Sn=3322×11+32×12

⇒Sn=6699

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About this question

This is a previous-year question from JEE Main 2024, 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.