JEE Main 2024MathematicsSequences and SeriesMediumMCQ

JEE Main 2024 — Sequences and Series Question with Solution

JEE Main 2024 (29 Jan Shift 2)

Question

If each term of a geometric progression a1,a2,a3,… with a1=18 and a2≠a1, is the arithmetic mean of the next two terms and Sn=a1+a2+…+an, then S20-S18 is equal to

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Show full solutionCorrect option: D
Correct answer
D-215

Step-by-step explanation

Let GP: a, ar, ar2, ar3,...

Now, given: 2ar=ar2+ar3

⇒2=r+r2

⇒r2+r-2=0

⇒r+2r-1=0

⇒r=-2, 1 Since GP is not constant so r=1 is rejected

⇒r=-2

⇒S20-S18=a1-r201-r-a1-r181-r

⇒S20-S18=ar18-r201-r

⇒S20-S18=218-2208×3

⇒S20-S18=2181-424

⇒S20-S18=-215

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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.