Discussion Forum



1)

Three positive numbers from an increasing GP. If the middle term on this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is 


A) $\sqrt{2}+\sqrt{3}$

B) $3+\sqrt{2}$

C) $2-\sqrt{3}$

D) $2+\sqrt{3}$

Answer:

Option D

Explanation:

Let a,ar, ar2 are in GP (r>1)

 On multiplying middle team by 2, a, 2ar, ar2 are in AP.

  $\Rightarrow$   $4ar=a+ar^{2}$

$\Rightarrow$     $r^{2}-4r+1=0$

$\Rightarrow$        $r=\frac{4\pm\sqrt{16-4}}{2}= 2\pm\sqrt{3}$

$\Rightarrow$   $r=2+\sqrt{3}$   [ $\because$  AP is increasing ]