Answer
$$183$$
Work Step by Step
$$\eqalign{
& \sum\limits_{i = 1}^5 {3{{\left( { - 3} \right)}^{i - 1}}} \cr
& {\text{Let }}{a_n} = 3{\left( { - 3} \right)^{i - 1}} \cr
& {a_1} = 3{\left( { - 3} \right)^{1 - 1}} = 3 \cr
& {a_2} = 3{\left( { - 3} \right)^{2 - 1}} = - 9 \cr
& {a_3} = 3{\left( { - 3} \right)^{3 - 1}} = 27 \cr
& {a_4} = 3{\left( { - 3} \right)^{4 - 1}} = - 81 \cr
& {a_5} = 3{\left( { - 3} \right)^{5 - 1}} = 243 \cr
& {\text{Then,}} \cr
& \sum\limits_{i = 1}^5 {3{{\left( { - 3} \right)}^{i - 1}}} = 3 - 9 + 27 - 81 + 243 \cr
& {\text{Simplifying}} \cr
& \sum\limits_{i = 1}^5 {3{{\left( { - 3} \right)}^{i - 1}}} = 183 \cr} $$
