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