The sum to infinity of a GP is 100, find its first term if the common ratio is -12

The sum to infinity of a GP is 100, find its first term if the common ratio is -12

Answer Details

S∞ ${}_{\infty }$ = a1−r $\frac{a}{1-r}$ since 1 > r

S∞ ${}_{\infty }$ = 100, r = −12 $\frac{-1}{2}$, a = ?

100 = a1−−12 $\frac{a}{1-\frac{-1}{2}}$ = a32 $\frac{a}{\frac{3}{2}}$ ( - - = +)

a = 100 x 32 $\frac{3}{2}$ = 150

Therefore, the first term (a) = 150