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

1 Answer
Nov 9, 2015

Answer:

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#