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. Not a sequence
2. Some other sequence
3. Geometric sequences
4. Arithmetic sequence

Answer 1

To classify the list of numbers \(9, 4, -1, -6, \ldots\), we need to examine the differences between consecutive terms:

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

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

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

Since the difference between each consecutive pair of terms is constant (-5), this list of numbers forms an arithmetic sequence.

Thus, the correct classification is: 4. Arithmetic sequence