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

arithmetic sequence
arithmetic sequence

some other sequence
some other sequence

not a sequence
not a sequence

geometric sequence

Answer 1

To determine the type of sequence represented by the numbers \(9, 4, -1, -6, \ldots\), let's analyze the differences and ratios:

Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant.

• The difference between the first term (9) and the second term (4) is \(4 - 9 = -5\).
• The difference between the second term (4) and the third term (-1) is \(-1 - 4 = -5\).
• The difference between the third term (-1) and the fourth term (-6) is \(-6 - (-1) = -5\).

Since the difference is consistent (-5) for all terms, this sequence is classified as an arithmetic sequence.

Final Classification:
Arithmetic Sequence