Question

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

9, 4, −1
−
1
, −6
−
6
, . . .

(1 point)
Responses

not a sequence
not a sequence

some other sequence
some other sequence

geometric sequence
geometric sequence

arithmetic sequence

Answer 1

To classify the given sequence \( 9, 4, -1, -6, \ldots \), we need to examine the differences or ratios between the terms to determine the type of sequence.

1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant. Let's calculate the differences:

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

Since the difference is consistent at \(-5\), this sequence is indeed an arithmetic sequence.

2. **Geometric Sequence**: In a geometric sequence, the ratio between consecutive terms is constant. Let's check the ratios:

- \( \frac{4}{9} \)
- \( \frac{-1}{4} \)
- \( \frac{-6}{-1} = 6 \)

The ratios are not constant, which eliminates it being a geometric sequence.

Since the sequence has a constant difference, we classify it as an **arithmetic sequence**.

Therefore, the answer is:

**arithmetic sequence**