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

some other sequence
some other sequence

arithmetic sequence
arithmetic sequence

geometric sequence
geometric sequence

not a sequence

Answer 1

To determine the type of sequence represented by the list of numbers \(9, 4, -1, -6, \ldots\), let’s analyze the differences between consecutive terms:

1. \(4 - 9 = -5\)
2. \(-1 - 4 = -5\)
3. \(-6 - (-1) = -5\)

Since the difference between consecutive terms is constant (\(-5\)), the sequence is classified as an arithmetic sequence.

So the correct response is:

arithmetic sequence