Three positive numbers form an increasing G.P. If the middle term in this G.P. Is doubled , the new numbers are in A.P. Then the common ratio of the G.P. Is?

Answer 1

If the first is a, then the 2nd is ar
In the AP, then,

2ar-a = ar^2-2ar
r^2 - 4r + 1 = 0
r = 2±√3
Since we know r>0, r=2+√3

check:
without loss of generality, w can take a=1. Then we have

GP: 1, 2+√3, 7+4√3
if we double the 2nd term, we have
1, 4+2√3, 7+4√3
and the common difference is 3+2√3