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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
Source: WAEC / JAMB / NECO Classroom Archive (Record #70192)