# Is the following a geometric sequence 1, -2, 4, -8, 16,…?

Nov 25, 2015

The terms listed are consistent with being a geometric sequence with initial term $1$ and common ratio $- 2$

#### Explanation:

The ratio of any two successive terms listed is $- 2$, so this can be a geometric sequence. I say can be because we do not know what the following terms are.

For example, the same terms are given by the formula:

a_n = 1/(0!)-3/(1!)(n-1)+9/(2!)(n-1)(n-2)

-27/(3!)(n-1)(n-2)(n-3)+81/(4!)(n-1)(n-2)(n-3)(n-4)

but this formula would make ${a}_{6} = 211$ rather than $- 32$