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

Let the three numbers be a/r, a, ar. As the numbers form  and increasing G.P., so, r>1. It is given that a/r. 2a, ar are in A.P. Hence,4a=ar+ar⇒r2−4r+1=0⇒r=2±3      =2+3 [∵r>1]