How do you find the 5th term of the sequence in which $t_1 = 8$ and $t_n = -3t_n-1$ ?

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Answer 1 · 2015-12-16T04:09:38

$t_5 = 648$

Given the sequence $t_1 = 8, t_n = -3t_(n-1)$ we have

$t_1 = 8$

$t_2 = -3t_1 = -24$

$t_3 = -3t_2 = 72$

$t_4 = -3t_3 = -216$

$t_5 = -3t_4 = 648$

Note that in general, as every term after the first is just $-3$ multiplied by the previous term, we can express the $n^(th)$ term directly as

$t_n = (-3)^(n-1)t_1 = (-3)^(n-1)*8$

In general, a sequence of the form

$a, ar, ar^2, ar^3, ..., ar^n, ...$

How do you find the 5th term of the sequence in which t_1 = 8t_1 = 8 and t_n = -3t_n-1t_n = -3t_n-1?