ANSWER:
[tex]a_4=-32[/tex]STEP-BY-STEP EXPLANATION:
We have that the formula of the geometric sequence has the following form:
[tex]\begin{gathered} a_n=a_1\cdot r^{n-1} \\ \end{gathered}[/tex]We have the following information
[tex]\begin{gathered} f(1)=4 \\ \text{therefore:} \\ a_1=4 \\ f(n)=f(n-1)\cdot-2 \\ \text{therefore:} \\ r=-2 \\ \text{replacing} \\ a_n=4\cdot(-2)^{n-1} \end{gathered}[/tex]In the case that n = 4, we replace
[tex]\begin{gathered} a_4=4\cdot(-2)^{4-1} \\ a_4=4\cdot-8 \\ a_4=-32 \end{gathered}[/tex]