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

Options

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

Answer

d

Explanation

Let a,ar,`ar^(2)` be in GP `(r gt 1)`
On multiplying middle term by 2 , then a, 2ar , `ar^(2)` are in AP.
` rArr 4ar = a+ ar^(2)`
` rArr r^(2) - 4r +1 = 0 ` ,brgt ` rArr r = (4pmsqrt(16-4))/2 = 2 pm sqrt(3)`
` rArr r = 2 + sqrt(3) " " [ :' "AP is increasing"]`