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Three positive numbers form an increasin...

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

A

`sqrt2 + sqrt3`

B

`3 + sqrt2`

C

`2 - sqrt3`

D

`2 + sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `a, ar, ar^(2)` are in GP, where `(r gt 1)`
On multiplying middle term by 2, we have
`a, 2ar, ar^(2)` are in an AP.
`rArr 4ar = a + ar^(2)`
`rArr r^(2) - 4r + 1 = 0`
`rArr r = (4 +- sqrt(16 -4))/(2) = 2 +- sqrt3`
`rArr r = 2 + sqrt3` [since, AP is increasing]
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