How many terms of the series 3, -6, +12, - 24, + ..... are needed to make a total of 1-28?

How many terms of the series 3, -6, +12, - 24, + ..... are needed to make a total of 1-28?

Answer Details

3, -6, +12, -24
a = 3, r = -2
$8n=\frac{a(1-r^n)}{1-r}\therefore 1-2^8=\frac{3(1-(-2^{n-1}\left)\right)}{1-(-2)}1-2^8=\frac{3(1-(-2^{n-1}\left)\right)}{3}$
1-28 = 1-(-2)n-1
-28 = -2n-1
8 = n-1
n = 9