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

Let numbers in G.P. be a, ar, ar^2
Now, 2(2ar) = a + ar^2 [∵a≠0]
⇒4r = 1 + r^2
⇒r^2 − 4r + 1 = 0
We have a formula for solving quadratic equation ax^2 + bx + c = 0 is x = −b ± √b^2 − 4ac / 2a
⇒r = 4 ± √16 − 4 / 2
⇒r = 4 ± √12 / 2
⇒r = 4 ± 2√3 / 2
⇒r = 2 ± √3
r = 2 + √3 (∵ 2 − √3 < 1, so for r = 2 − √3, the G.P. will not be increasing)