Question

The geometric series $-4+16-64+\mathrm{256....}$, $S_n=52428$. Find the number of terms.

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is D $8$

First term, $a$ is $-4$
Common ratio, $r=-4$
$S_n=\frac{a(1-r^n)}{1-r}$
$\Rightarrow S_n=\frac{-4(1-(-4{)}^n)}{1-(-4)}$
$\Rightarrow -65535=1+4^n$
$\Rightarrow 65536=4^n$
$\Rightarrow 4^8=4^n$
So, $n=8$