What is the 9th term of the geometric sequence where a1 = -8 and a6 = -8,192?

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Answer 1 · 2016-05-31T18:23:01

We must first find the common ratio $r$ .

The $nth$ term of a geometric series is given by $t_n = a xx r^(n - 1)$ . We know $a$ , the first term, we know $t_6$ , and therefore we know $n (6)$

$-8192 = -8 xx r^(6 - 1)$

$-8192/-8 = r^5$

$1024 = r^5$

$root(5)(1024) = r$

$4 = r$

Now, we can reuse the formula $t_n = a xx r^(n - 1)$ to find the 9th term.

$t_9 = -8 xx 4^(9 - 1)$

$t_9 = -8 xx 4^8$

$t_9 = -524288$

Therefore, $t_9$ is -524 288.

Practice exercises:

Determine the 11th term of a geometric sequence where the first term is 27 and $t_4$ is 1.
Determine the 7th term of a geometric sequence where the second term is 3 and the fifth is 375.

Hopefully this helps, and Good luck!