Question

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

Answer 1

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`