What is s_n of the geometric series with a_1=4, a_n=256, and n=4?

The sum is $340$.
Since the $n t h$ term is given as $256$ but $n$ is given as $4$, that means $256$ is the $4 t h$ term. But the $4 t h$ term of a GP equals $a {r}^{3}$, where a is the first term and $r$ is the common ratio of the GP. Dividing $256$ by the first term (which is given as $4$) shows us that ${r}^{3} = \frac{256}{4} = 64$.
If ${r}^{3} = 64$, then the common ratio $r$ must equal $4$ as well. This gives us all the information we need to use the formula for the sum of a GP, $S = \frac{a \left({r}^{n} - 1\right)}{r - 1}$.
In this case, $S = \frac{4 \left({4}^{4} - 1\right)}{4 - 1} = \frac{4 \left(256 - 1\right)}{3} = \frac{1020}{3} = 340$.