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

geometric sequence
geometric sequence

arithmetic sequence
arithmetic sequence

not a sequence
not a sequence

Answer 1

To classify the sequence \(9, 4, -1, -6, \ldots\), we will check the differences between consecutive terms.

• The difference between the first two terms: \(4 - 9 = -5\)
• The difference between the second and third terms: \(-1 - 4 = -5\)
• The difference between the third and fourth terms: \(-6 - (-1) = -5\)

Since the difference between each pair of consecutive terms is constant (equal to \(-5\)), this sequence is classified as an arithmetic sequence.

So, the correct response is:

arithmetic sequence.