Answer
$$r = 4{\text{ and }}{a_n} = {4^n}$$
Work Step by Step
$$\eqalign{
& {a_1} = 4,{a_2} = 16,{a_3} = 64,{a_4} = 256,... \cr
& {\text{to verify that the sequence is geometric}}{\text{, divide each term except the first by }} \cr
& {\text{the preceding term}} \cr
& \frac{{256}}{{64}} = \frac{{64}}{{16}} = \frac{{16}}{4} = 4 \cr
& {\text{the ratio is constant}}{\text{, ao the sequence is geometric with }}r = 4 \cr
& {\text{The general term of a geometric sequence is }}{a_n} = {a_1}{r^{n - 1}} \cr
& {\text{then}} \cr
& {a_n} = 4{\left( 4 \right)^{n - 1}} \cr
& {\text{simplifying}} \cr
& {a_n} = {4^n} \cr} $$
