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Three positive numbers form an increasin...

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

A

`2-sqrt(3)`

B

`2+sqrt(3)`

C

`sqrt(2)+sqrt(3)`

D

`3+sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let a, ar, `ar^2` are in `GP because underset(r gt 1)(GP)` is increasing
New numbers a, `ar^2` are in AP.
`:." "4ar = a+ar^2" "rArr" "r^2 - 4+1=0`
Hence, `r=(4 -+ sqrt(16-4))/2 = 2+sqrt3" "[because r gt 1 ]`
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