Question

Find $S_n$ for each of the geometric series described below:
$a=2,t_6=486,n=6$

Answer 1

Here $a=2,t_6=486,n=6$
Now $t_6=2(r{)}^5=486$
$\Rightarrow r^5=243$

$\Rightarrow r=3$.
Now, $S_n=\frac{a(r^n-1)}{r-1}$ if $r\ne 1$
Thus, $S_6=\frac{2(3^6-1)}{3-1}=3^6-1=728$