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The sum to infinity of a GP is 100, find its first term if the...

Mathematics
JAMB 2024

The sum to infinity of a GP is 100, find its first term if the common ratio is -\(\frac{1}{2}\)

  • A. 150
  • B. 155
  • C. 160
  • D. 165
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Correct Answer: Option A
Explanation

S\(_∞\) = \(\frac{a}{1- r}\) since 1 > r

S\(_∞\) = 100, r = \(\frac{-1}{2}\), a = ?

100 = \(\frac{a}{1- \frac{-1}{2}}\) = \(\frac{a}{\frac{3}{2}}\) ( - - = +)

a = 100 x \(\frac{3}{2}\) = 150

Therefore, the first term (a) = 150

There is an explanation video available below.


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Explanation Video

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