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The sum to infinity of a geometric progression is \(-\frac{1}{10}\) and the first term is...

Mathematics
JAMB 2012

The sum to infinity of a geometric progression is \(-\frac{1}{10}\) and the first term is \(-\frac{1}{8}\). Find the common ratio of the progression.
  • A. \(-\frac{1}{5}\)
  • B. \(-\frac{1}{4}\)
  • C. \(-\frac{1}{3}\)
  • D. \(-\frac{1}{2}\)
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Correct Answer: Option B
Explanation
Sr = \(\frac{a}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8} \times \frac{1}{1 - r}\)

\(-\frac{1}{10}\) = \(\frac{1}{8(1 - r)}\)

\(-\frac{1}{10}\) = \(\frac{1}{8 - 8r}\)

cross multiply...

-1(8 - 8r) = -10

-8 + 8r = -10

8r = -2

r = -1/4

There is an explanation video available below.


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Explanation Video

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