Question

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

not a sequence
not a sequence

arithmetic sequence
arithmetic sequence

some other sequence
some other sequence

geometric sequence

Answer 1

To classify the sequence given as \(9, 4, -1, -6, \ldots\), we need to check for the characteristics of arithmetic and geometric sequences.

1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant. Let's calculate the differences between the terms:
- \(4 - 9 = -5\)
- \(-1 - 4 = -5\)
- \(-6 - (-1) = -5\)

Since the difference between each of the consecutive terms is the same (i.e., \(-5\)), this is an arithmetic sequence.

2. **Geometric Sequence**: In a geometric sequence, the ratio between consecutive terms is constant. Let's calculate the ratios:
- \(4 / 9\) (not consistent)
- \(-1 / 4\) (not consistent)
- \(-6 / -1 = 6\) (not consistent)

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

Based on the analysis, the correct classification of the sequence \(9, 4, -1, -6, \ldots\) is:

**Arithmetic sequence**.