The sum to infinity of a GP is 100, find its first term if the common ratio is -\(\frac{1}{2}\)
-
150
- 155
- 160
- 165
The correct answer is: 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
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