Given $S_n=3(2^n+1)$, find the fourth term.
I believe I can find the first term, $a$, assuming n=1 is the beginning. $3(2^1+1)=9$
To find the fourth term, I have tried to do it by subtracting $S_4$ and $S_3$. This gives me 24.
Is this mathematically sound? When I try to determine the common ratio from this, namely $24=ar^3$, $r=1.386722549$. However, when I try to find another term, say $t_3$, $S_3-S_2 \neq ar^2$. Therefore, I must be doing something wrong here; specifically, finding the common ratio from only one equation is probably incorrect.
So: 1) Is 24 the third term? 2) If so, how do I find the common ratio from this?