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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.
  • 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, 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}})

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