Question

Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of G.P. is

• A.
• B.
• C.
• D. 2

Answer 1

The correct option is B

Three numbers in G.P. are $\frac{a}{r}$, a, ar then $\frac{a}{r}$, 2a, ar in A.P. as given

∴ 2(2a) = a(r + $\frac{1}{r}$)

or, $r^2$ - 4r + 1 = 0 or r = 2 ± $\sqrt{3}$

or, r = 2 + $\sqrt{3}$ as r > 1 for an increasing G.P.