JEE Main 2020MathematicsSequences and SeriesMediumMCQ

JEE Main 2020 — Sequences and Series Question with Solution

JEE Main 2020 (05 Sep Shift 1)

Question

If 32sin2α-1,14 and 34-2sin2α are the first three terms of an A.P. for some α , then the sixth term of this A.P. is

Choose an option

Show full solutionCorrect option: A
Correct answer
A66

Step-by-step explanation

If a, b, c are in AP, then b is A.M of a & c. 

∴ 2 b=a+c

⇒28=32sin2α-1+34-2sin2α

Putting, 32sin2α=x we get,

28=x3+81x⇒x2-84x+243=0

⇒(x-3)(x-81)=0

∴ 32sin2α=3 or 34

sin2α=12, ∵sin2α≠2

Terms are 1,14,27,…… then

T6=1+5(13)=66

 

 

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Sequences and Series chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.