Question

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

3, 1, –1, –3, ...
4, 3, –3, –4, …
2, -1, ½,-¼ ...

Answer 1

3, 1, –1, –3, ... arithmetic

4, 3, –3, –4, … neither

2, -1, ½,-¼ ... geometric

Explanation:

3, 1, –1, –3, ...

We are subtracting 2 from the previous term

This is an arithmetic sequence

4, 3, –3, –4, …

There is no number that we can add to each term to get the next

There is no number that we can multiply to each term to get the next

neither

2, -1, ½,-¼ ...

We can multiply by -1/2 to get the next term

This is a geometric sequence