Question

Question
Classify the following list of numbers as an arithmetic sequence, a geometric sequence, some other sequence, or not a sequence.

9, 4, −1
, −6
, . . .

(1 point)
Responses

not a sequence
not a sequence

arithmetic sequence
arithmetic sequence

some other sequence
some other sequence

geometric sequence

Answer 1

To classify the given list of numbers \(9, 4, -1, -6, \ldots\), let's first check if it's an arithmetic sequence:

An **arithmetic sequence** is one where the difference between consecutive terms is constant.

1. The difference between the first term (9) and the second term (4) is:
\[
4 - 9 = -5
\]

2. The difference between the second term (4) and the third term (-1) is:
\[
-1 - 4 = -5
\]

3. The difference between the third term (-1) and the fourth term (-6) is:
\[
-6 - (-1) = -5
\]

Since the difference between each pair of consecutive terms is constant at \(-5\), we can conclude that this is an **arithmetic sequence**.

Thus, the correct classification is:

**arithmetic sequence**