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

geometric sequence
geometric sequence

not a sequence
not a sequence

some other sequence
some other sequence

arithmetic sequence

Answer 1

To determine the type of sequence, we need to analyze the differences or ratios between consecutive terms.

The given sequence is: 9, 4, -1, -6, ...

1. Checking for an arithmetic sequence:
   • The difference between the first and second terms: 4 - 9 = -5
   • The difference between the second and third terms: -1 - 4 = -5
   • The difference between the third and fourth terms: -6 - (-1) = -5

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

So, the classification is:

arithmetic sequence