Answer
$-40$
Work Step by Step
The sum of the first $n$ terms of a geometric sequence can be found using the formula:
$$S_n=\dfrac{a_1(1-r^n)}{1-r}; r \ne 1$$
where, $r$ is the common ratio, $r$ and can be computed as the quotient of a term and the term preceeding it.
From the given series, we have: $a_1=-1$ and $r=3$
Plug these values in the formula above to obtain:
$$S_n=\dfrac{-1(1-3^n)}{1-3}$$
With $n=4$ the equation above yields:
$$S_4=\dfrac{-1(1-3^4)}{1-3}=-\dfrac{-1(-80)}{-2}=-40$$
Hence: $S_4=-40$.
