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.

A.
(frac{1}{4}) 
B.
(sqrt{frac{3}{2}}) 
C.
(frac{1}{sqrt{3}}) 
D.
(frac{1}{sqrt{2}})
Correct Answer: Option B
Explanation
Let the G.p be a, ar, ar^{2}, S^{3} = (frac{1}{2})S
a + ar + ar^{2} = (frac{1}{2})((frac{a}{1 – r}))
2(1 + r + r)(r – 1) = 1
= 2r^{3} = 3
= r^{3} = (frac{3}{2})
r((frac{3}{2}))^{(frac{1}{3})} = (sqrt{frac{3}{2}})