The sum of the first three terms of a geometric... - JAMB Mathematics 1998 Question
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
\(\frac{1}{\sqrt{2}}\)
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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}})
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