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
\(\frac{1}{\sqrt{2}}\)
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(\(\frac{3}{2}\))\(\frac{1}{3}\) = \(\sqrt{\frac{3}{2}}\)
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