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Question

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


  1. 2+3

  2. 23

  3. 2+3

  4. 3+2


Solution

The correct option is A

2+3


Let a,ar,ar2 are in GP, where (r > 1)
On multiplying middle term by 2, we have
a,2ar,ar2 are in an AP
4ar=a+ar2
r24r+1=0
r=4±1642
=2±3
r=2+3   [since, AP is increasing]

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