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 the G.P. is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the three numbers be a/r, a, ar. As the numbers form an increasing G.P., so, r >1.It is given that a/r, 2a, ar are in A.P. Hence,

$4a=\frac{a}{r}+ar$

$\Rightarrow r^2-4r+1=0$

$\Rightarrow r=2\pm \sqrt{3}$

$=2+\sqrt{3}[\because r>1$