What is the 8th term of the geometric sequence –1, 4, –16, …?

1 Answer
sente
Nov 9, 2015

The 8th term is -16384

Explanation:

A geometric sequence is a sequence of the form
a, ar, ar^2, ar^3, ...
where a is the initial value and r is a common ratio between terms.

Because of this, given any two successive terms of the sequence, you can find r by dividing the later term by the previous one:
(ar^n)/(ar^(n-1)) = r

In the given sequence, then, we can find the ratio by dividing the second term by the first:
4/-1 = -4

Finally, to obtain the 8th term in the sequence, we can either calculate the term by multiplying successive terms by the ratio repeatedly, or directly as (-1)(-4)^7

In either case, we arrive at the 8th term being -16384

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