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

not a sequence
not a sequence

some other sequence
some other sequence

geometric sequence

Answer 1

To classify the sequence \(9, 4, -1, -6, \ldots\), we need to examine the differences and ratios between consecutive terms.

1. Check for Arithmetic Sequence: An arithmetic sequence has a constant difference between consecutive terms.

   • \(4 - 9 = -5\)
   • \(-1 - 4 = -5\)
   • \(-6 - (-1) = -5\)

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

Therefore, the correct classification is:

arithmetic sequence