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) not a sequence arithmetic sequence geometric sequence some other sequence

Explanation:

Step1: Check for arithmetic sequence (common difference)

To find the common difference \( d \) in an arithmetic sequence, we calculate the difference between consecutive terms.
First, \( 4 - 9 = -5 \)
Second, \( -1 - 4 = -5 \)
Third, \( -6 - (-1) = -5 \)
Since the difference between consecutive terms is constant (\( d = -5 \)), we check if it could be geometric.

Step2: Check for geometric sequence (common ratio)

To find the common ratio \( r \) in a geometric sequence, we calculate the ratio between consecutive terms.
First, \( \frac{4}{9} \approx 0.444 \)
Second, \( \frac{-1}{4} = -0.25 \)
Third, \( \frac{-6}{-1} = 6 \)
The ratios are not constant, so it is not a geometric sequence.

Since the common difference is constant, it is an arithmetic sequence.

Answer:

arithmetic sequence