Answer
$${\text{ }}{a_n} = - 8{\left( {\frac{1}{2}} \right)^{n - 1}},{\text{ and }}{a_4} = - 1$$
Work Step by Step
$$\eqalign{
& {a_1} = - 8,\,\,\,{a_7} = - \frac{1}{8} \cr
& {\text{We obtain }}{a_7}{\text{ by multiplying }}{a_1}{\text{ by the common ratio six times}} \cr
& {a_7} = {a_1}{r^6} \cr
& - \frac{1}{8} = \left( { - 8} \right){r^6} \cr
& \frac{1}{{64}} = {r^6} \cr
& r = \frac{1}{2} \cr
& {\text{Then }}{a_n} = {a_1}{r^{n - 1}} \cr
& {\text{ }}{a_n} = - 8{\left( {\frac{1}{2}} \right)^{n - 1}} \cr
& {\text{Find }}{a_4} \cr
& {\text{ }}{a_4} = - 8{\left( {\frac{1}{2}} \right)^{4 - 1}} \cr
& {\text{ }}{a_4} = - 1 \cr
& \cr
& {\text{ }}{a_n} = - 8{\left( {\frac{1}{2}} \right)^{n - 1}},{\text{ and }}{a_4} = - 1 \cr} $$
