G.P

The sum of terms of a GP is given by

$s=\dfrac{a_1-a_1r^n}{1-r}$ $\implies$ $189=\dfrac{3-3r^n}{1-r}$ $\implies$ $189-189r=3-3r^n$ $\implies$ $186=-3r^n+189r$ $\color{#D61F06}(1)$

The $n^{th}$ term of a GP is given by

$a_n=a_1r^{n-1}$ $\implies$ $96=3r^{n-1}$ $\implies$ $32r^{n-1}$ $\implies$ $32=\dfrac{r^n}{r}$ $\implies$ $32r=r^n$ $\color{#D61F06}(2)$

Substituting $\color{#D61F06}(2)$ in $\color{#D61F06}(1)$ , we have

$186=-3(32r)+189r$ $\implies$ $186=-96r+189r$ $\implies$ $186=93r$ $\implies$ $r=2$

Solve for $n$ in $\color{#D61F06}(2)$ by substituting $r=2$ ,

$32(2)=2^n$ $\implies$ $64=2^n$ $\implies$ $2^6=2^n$ $\implies$ $\boxed{n=6}$

The Geometric Progression is $3,6,12,24,48,96$ .

this term will be 3, 6, 12, 24, 48, 96................

just multiply the previous term by 2.