Finding the sum of $\sum_{i=0}^{2n} (-2)^i$

Question

I am aware that the series will have a sequence of $1, -2, 4, -8, 16, \ldots$ which is the number before it, added to the next multiple of $3$. The difference of $1$ and $-2$ being $3$ and the difference of $-2$ and $4$ being $6$.

Answer 1

Relevant formula:

$$\sum_{k=0}^{n-1}r^k= \frac{1-r^n}{1-r}$$

You might like to read up on Geometric series.