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

Question

9, 4, −1
, −6
, . . .

(1 point)
Responses

geometric sequence
geometric sequence

arithmetic sequence
arithmetic sequence

some other sequence
some other sequence

not a sequence

Answer 1

To determine the classification of the sequence given (9, 4, −1, −6, ...), we should check if it's an arithmetic sequence or a geometric sequence.

1. Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant.
   • Difference between 4 and 9: 4 - 9 = -5
   • Difference between -1 and 4: -1 - 4 = -5
   • Difference between -6 and -1: -6 - (-1) = -5

Since the difference is consistent at -5, this sequence is an arithmetic sequence.

2. Geometric Sequence: In a geometric sequence, the ratio between consecutive terms is constant.
   • Ratio between 4 and 9: 4 / 9 ≈ 0.444
   • Ratio between -1 and 4: -1 / 4 = -0.25
   • Ratio between -6 and -1: -6 / -1 = 6

These ratios are not consistent, so it is not a geometric sequence.

Based on the evaluations, the correct classification of the sequence is:

arithmetic sequence.