Question

Classify the following list of numbers as an arithmetic sequence, a geometric sequence, or neither.

9,4,-1,-6

(1 point)
Responses

Neither
Neither

Not enough information given
Not enough information given

Arithmetic
Arithmetic

Geometric

Answer 1

To classify the sequence 9, 4, -1, -6, we can check the differences between consecutive terms to see if it's an arithmetic sequence, and we can check the ratios of consecutive terms to see if it's a geometric sequence.

**Arithmetic Sequence:**
An arithmetic sequence is one where the difference between consecutive terms is constant.

- 4 - 9 = -5
- -1 - 4 = -5
- -6 - (-1) = -5

The difference between consecutive terms is consistently -5, so the numbers form an arithmetic sequence.

**Geometric Sequence:**
A geometric sequence is one where the ratio of consecutive terms is constant.

- 4 / 9 ≈ 0.4444
- -1 / 4 = -0.25
- -6 / -1 = 6

The ratios are not constant, so this is not a geometric sequence.

**Conclusion:**
The sequence 9, 4, -1, -6 is classified as **Arithmetic**.