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

Options

A. `2-sqrt(3)`
B. `2+sqrt(3)`
C. `sqrt(2)+sqrt(3)`
D. `3+sqrt(2)`

Answer

B

Explanation

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 ]`