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
geometric sequence

Answer 1

To classify the sequence 9, 4, −1, −6, we need to analyze the differences between the successive terms:

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 consecutive term is constant (-5), this sequence is classified as an arithmetic sequence.

So, the correct response is:

arithmetic sequence