Question

# Three positive numbers form an increasing GP. If the middle term of the GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is  (IIT JEE Main 2014)

A
2+3
B
3+2
C
23
D
2+3

Solution

## The correct option is D 2+√3Let a, ar, ar2 are in GP.  If the middle term of the GP is doubled, then new numbers are in AP.  ⇒a,2ar,ar2 are in AP.  ⇒4ar−a+ar2 ⇒r2−4r+1=0 ⇒r−2±√3 Since the series is an increasing GP so,  ⇒r−2+√3

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