Question

Determine whether each of the following is a geometric sequence, arithmetic sequence, or neither.

3, 1, –1, –3,..

Answer 1

Arithmetic has constant differences.
Geometric has constant ratios.

3, 1, –1, –3,..

1-3 = -2
-1-1 = -2
-3 - (-1) = -2

And we see a Common Difference. This is arithmetic.
Knowing that it is Arithmetic, it cannot be Geometric, but let's do it, anyway.

3, 1, –1, –3,..

1/3 = 1/3
-1/1 = -1
-3/(-1) = 3

That is NOT a constant Ratio. It is Not Geometric.

If it fails both tests, it's neither.

Answer 2

nice explanation @tkhunny ;) :)