Question

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

Answer 1

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`