Question

Classify the following list of numbers as an arithmetic sequence, a geometric sequence, some other sequence, or not a sequence.

9, 4, −1, −6, . . .

(1 point)
Responses

geometric sequence
geometric sequence

not a sequence
not a sequence

some other sequence
some other sequence

arithmetic sequence

Answer 1

To determine the classification of the given sequence (9, 4, −1, −6, ...), we need to check if it follows the rules for an arithmetic or a geometric sequence.

1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant.

Let's find the differences:
- 4 - 9 = -5
- -1 - 4 = -5
- -6 - (-1) = -5

The difference between each pair of consecutive terms is the same (-5), so this is an arithmetic sequence.

2. **Geometric Sequence**: In a geometric sequence, the ratio of consecutive terms is constant.

Let's find the ratios:
- 4 / 9 = 4/9
- -1 / 4 = -1/4
- -6 / -1 = 6

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

Therefore, the correct classification of the sequence (9, 4, −1, −6, ...) is:

**arithmetic sequence**.