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

geometric sequence
geometric sequence

not a sequence
not a sequence

some other sequence

Answer 1

To classify the sequence 9, 4, −1, −6, let's first determine if it is arithmetic or geometric.

1. Arithmetic Sequence: A sequence is arithmetic if the difference between consecutive terms is constant.

   • The difference between the first and second term: 4 - 9 = -5
   • The difference between the second and third term: -1 - 4 = -5
   • The difference between the third and fourth term: -6 - (-1) = -5

   Since the difference is constant (-5) for all terms, this sequence is an arithmetic sequence.

2. Geometric Sequence: A sequence is geometric if the ratio of consecutive terms is constant.

   • The ratio between the first and second term: 4 / 9 ≈ 0.444
   • The ratio between the second and third term: -1 / 4 = -0.25
   • The ratio between the third and fourth term: -6 / -1 = 6

   The ratios are not constant, so it is not a geometric sequence.

Since the sequence has been determined to be arithmetic, the correct classification is:

arithmetic sequence.