Question

Find the 5th term of the sequence in which t1 = 8 and tn-1 = -3tn-1

Answer 1

`\bf t_1=8\qquad \qquad t_n=-3\cdot t_(n-1)`

is a notational way of saying

the first term's value is 8

and any subsequent terms, are obtained by simply multiplying -3


`\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}`