One way to do it is to find an explicit formula for the [tex]n[/tex]th term.
[tex]t_n=-3t_{n-1}=-3(-3t_{n-2})=(-3)^2t_{n-2}=(-3)^2(-3t_{n-3})=(-3)^3t_{n-3}=\cdots[/tex]
The pattern suggests that the [tex]n[/tex]th term is given by [tex]t_n=(-3)^{n-1}t_1[/tex], and so the fifth term is [tex]t_5=(-3)^4t_1=648[/tex].
Another way to do it would be to plug [tex]t_1[/tex] into the recursive formula to find [tex]t_2[/tex], then [tex]t_3[/tex], and so on.
[tex]t_2=-3t_1=-24[/tex]
[tex]t_3=-3t_2=72[/tex]
[tex]t_4=-3t_3=-216[/tex]
[tex]t_5=-3t_4=648[/tex]
