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

arithmetic sequence
arithmetic sequence

not a sequence
not a sequence

some other sequence
some other sequence
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Answer 1

To classify the sequence 9, 4, −1, −6, we need to determine the relationship between the numbers.

1. **Arithmetic Sequence**: In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. Let's check the differences:
- 4 - 9 = -5
- -1 - 4 = -5
- -6 - (-1) = -5

The common difference is -5, so this sequence is an arithmetic sequence.

2. **Geometric Sequence**: In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. Let's check the ratios:
- 4 / 9 ≈ 0.44
- -1 / 4 = -0.25
- -6 / -1 = 6

Since the ratios are not constant, this sequence is not a geometric sequence.

Considering the checks above, the correct classification for the sequence 9, 4, −1, −6 is **arithmetic sequence**.