JEE Main 2020MathematicsSequences and SeriesMediumMCQ

JEE Main 2020 — Sequences and Series Question with Solution

JEE Main 2020 (09 Jan Shift 2)

Question

Let an be the nth term of a G.P. of positive terms. If ∑n=1100a2n+1=200 and ∑n=1100a2n=100, then ∑n=1200an is equal to:

Choose an option

Show full solutionCorrect option: D
Correct answer
D150

Step-by-step explanation

Let GP is a,ar,ar2…

∑n=1100a2n+1=a3+a5+…a201=200⇒ar2(r200-1)r2-1=200   …1

∑n=1100a2n=a2+a4+…a200=100=arr200-1r2-1=100     …2

Form 1 and 2, r=2

adding both,

⇒a2+a3+…a200+a201=300⇒ra1+…a200=300

∑n=1200300r=150

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About this question

This is a previous-year question from JEE Main 2020, 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.