Answer
$$\eqalign{
& - 2,4, - 8,16, - 32 \cr
& {\text{The sequence is geometric}} \cr} $$
Work Step by Step
$$\eqalign{
& {a_n} = {\left( { - 2} \right)^n} \cr
& {\text{Write the first five terms of the sequence}} \cr
& n = 1 \cr
& {a_1} = {\left( { - 2} \right)^1} = - 2 \cr
& \cr
& n = 2 \cr
& {a_2} = {\left( { - 2} \right)^2} = 4 \cr
& \cr
& n = 3 \cr
& {a_3} = {\left( { - 2} \right)^3} = - 8 \cr
& \cr
& n = 4 \cr
& {a_4} = {\left( { - 2} \right)^4} = 16 \cr
& \cr
& n = 5 \cr
& {a_5} = {\left( { - 2} \right)^4} = - 32 \cr
& \cr
& - 2,4, - 8,16, - 32 \cr
& {\text{The sequence is geometric}} \cr} $$
