[tex]\bf t_1=8\qquad \qquad t_n=-3\cdot t_{n-1}[/tex]
is a notational way of saying
the first term's value is 8
and any subsequent terms, are obtained by simply multiplying -3
[tex]\bf \begin{array}{ccllll}
n&term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1&t_1&8\\
2&t_2&-3\cdot t_{2-1}\\
&&-3\cdot t_1\\
&&-3\cdot 8\implies -24\\
3&t_3&-3\cdot t_{3-1}\\
&&-3\cdot t_2\\
&&-3\cdot -24\implies 72\\
4&t_4&-3\cdot t_{4-1}\\
&&-3\cdot t_3\\
&&-3\cdot 72\implies -216\\
5&t_5&-3\cdot t_{5-1}\\
&&-3\cdot t_4\\
&&-3\cdot -216\implies 648
\end{array}[/tex]
