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 Option:
B
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(\(\frac{3}{2}\))\(\frac{1}{3}\) = \(\sqrt{\frac{3}{2}}\)
a + ar + ar2 = \(\frac{1}{2}\)(\(\frac{a}{1 - r}\))
2(1 + r + r)(r - 1) = 1
= 2r3 = 3
= r3 = \(\frac{3}{2}\)
r(\(\frac{3}{2}\))\(\frac{1}{3}\) = \(\sqrt{\frac{3}{2}}\)