Given that
[tex]a_{n+1}=-4a_{n+2}[/tex] and [tex]a_1=2[/tex]
For n = 0,
[tex]a_1=-4a_2 \\ \\ 2=-4a_2 \\ \\ \Rightarrow a_2=-\frac{1}{2}[/tex]
common ratio = [tex]\frac{a_2}{a_1}=\frac{-\frac{1}{2}}{2}=-\frac{1}{4}[/tex]
4th term = [tex]a_4=a_1r^{4-1}=2(-\frac{1}{4})^3=2(-\frac{1}{64})=-\frac{1}{32}[/tex]
