The sum of the first three terms of a geometric progression is half its sum…

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.

Correct Answer: Option B

Explanation

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}})