The sum of the first three terms of a geometric progression is half its sum to infinity. Find the positive common ratio of the progression.

The sum of the first three terms of a geometric progression is half its sum to infinity. Find the positive common ratio of the progression.

Answer Details

Let the G.P be a, ar, ar2, S3 = $\frac{1}{2}$S
a + ar + ar2 = $\frac{1}{2}$($\frac{a}{1-r}$)
2(1 + r + r)(r - 1) = 1
= 2r3 = 3
= r3 = $\frac{3}{2}$
r($\frac{3}{2}$)$\frac{1}{3}$ = $\sqrt{\frac{3}{2}}$