Question

The value of $1+3+9+27+81+...+2187$ is

Answer 1

$1+3+9+27+81+...+2187$
The given series is G.P. with $a=1,r=3$
$\Rightarrow a{r}^{n-1}=2197$
$\Rightarrow 3^{n-1}=3^7$
$\Rightarrow n=8$
Sum $=\frac{a(r^n-1)}{r-1}$
$\therefore S=\frac{3^8-1}{3-1}=3280$