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.
- \(\frac{1}{4}\)
-
\(\sqrt{\frac{3}{2}}\)
- \(\frac{1}{\sqrt{3}}\)
- \(\frac{1}{\sqrt{2}}\)
The correct answer is: B
Explanation
Let the G.p be a, ar, ar2, S3 = \(\frac{1}{2}\)Sa + ar + ar2 = \(\frac{1}{2}\)(\(\frac{a}{1 - r}\))
2(1 + r + r)(r - 1) = 1
= 2r3 = 3
= r3 = \(\frac{3}{2}\)
r(\(\frac{3}{2}\))\(\frac{1}{3}\) = \(\sqrt{\frac{3}{2}}\)