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

not a sequence
not a sequence

geometric sequence
geometric sequence

some other sequence
some other sequence

arithmetic sequence

Answer 1

To determine the type of sequence defined by the numbers 9, 4, -1, -6, we first look for a pattern.

1. Calculate the differences between consecutive terms:

• From 9 to 4: \( 4 - 9 = -5 \)
• From 4 to -1: \( -1 - 4 = -5 \)
• From -1 to -6: \( -6 - (-1) = -5 \)

The difference between each pair of consecutive terms is -5, which is constant.

Since the difference is constant, this is classified as an arithmetic sequence.

So the correct response is:

arithmetic sequence