Answer
$${S_4} = - 40$$
Work Step by Step
$$\eqalign{
& {a_1} = - 1,\,\,\,\,r = 3 \cr
& {\text{Determine }}{S_4}{\text{ using }}{S_n} = \frac{{{a_1}\left( {1 - {r^n}} \right)}}{{1 - r}}\,\,\,\left( {{\text{where }}r \ne 1} \right) \cr
& {\text{Let }}n = 4 \cr
& {S_4} = \frac{{{a_1}\left( {1 - {r^4}} \right)}}{{1 - r}} \cr
& {S_4} = \frac{{ - 1\left( {1 - {3^4}} \right)}}{{1 - 3}} \cr
& {\text{Simplifying}} \cr
& {S_4} = - 40 \cr} $$
