JEE Main 2018MathematicsSequences and SeriesMediumMCQ

JEE Main 2018 — Sequences and Series Question with Solution

JEE Main 2018 (08 Apr)

Question

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 

12+2·22+32+2·42+52+2·62+…

If B-2A=100λ, then λ is equal to :

Choose an option

Show full solutionCorrect option: C
Correct answer
C248

Step-by-step explanation

Given series, 12+2·22+32+2·42+52+2·62+… 

Here, A=12+2·22+32+2·42+...20 terms

=12+ 22+32+42+...20 terms+22+42+ 62+...10 terms

=20·21·416 +410·11·216 

⇒A=4410

Similarly for B=12+22+33+...40 terms+22+42+62+...20 terms

⇒B=40×41×816+4×20×21×416

⇒B=33620

Now, B-2A=24800=100λ (Given)

⇒λ=248

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About this question

This is a previous-year question from JEE Main 2018, 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.