JEE Main 2015MathematicsSequences and SeriesMediumMCQ

JEE Main 2015 — Sequences and Series Question with Solution

JEE Main 2015 (11 Apr Online)

Question

The sum of the 3rd and the 4th terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7th term is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A 320

Step-by-step explanation

Let the 'G.P.' be

ar,a,ar,ar2

Given, 

ar·a·ar=1000

⇒a3=1000

⇒a=10

Also, ar+ar2=60

⇒10r+r2=60

⇒r+r2=6

⇒r2+r-6=0

⇒r-2 r+3=0

So, r=2 or r=-3

As 1st term is positive ∴  r=2

∴ G.P. is '5', '10', '20'.......

Hence, 7th term is 5·26=320.

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About this question

This is a previous-year question from JEE Main 2015, 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.