JEE Main 2014MathematicsSequences and SeriesMediumMCQ

JEE Main 2014 — Sequences and Series Question with Solution

JEE Main 2014 (06 Apr)

Question

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is :

Choose an option

Show full solutionCorrect option: B
Correct answer
B 2 + 3

Step-by-step explanation

Let the three numbers of the GP be a, ar and ar2 where r is the common ratio.
According to the given condition, a, 2ar and ar2 are in AP.

∴  2ar=a+ar22

∴  a+ar2=4ar

∴  r2+1=4r

∴  r2-4r+1=0

∴  r=4±16-42

         = 4 ± 2 3 2 = 2 ± 3

As it is an 'increasing' GP, r > 1.

∴  r=2+3.

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About this question

This is a previous-year question from JEE Main 2014, 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.