How To Write A Formula For The First N Terms of a Sequence? So I have the sequence $$\{5, 15, 45,\cdots\}$$ and I figured out that the formula to find a particular term is $$S_n = 5 \times 3^{n-1}$$ but how do I use this to find the sum of the first $n$ terms?

Hint. One may recall that, for $n=1,2,\cdots$,
$$
1+x+x^2+\cdots+x^{n-1}=\frac{1-x^{n}}{1-x}, \qquad x \neq 1.
$$
