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) Responses not a sequence not a sequence arithmetic sequence arithmetic sequence some other sequence some other sequence geometric sequence

Answer 1

To classify the given list of numbers: 9, 4, −1, −6, let's first check if it is an arithmetic or geometric sequence.

1. Arithmetic Sequence: An arithmetic sequence has a constant difference between consecutive terms.

   • The difference between the first two 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 is constant (-5) for all consecutive terms, this is an arithmetic sequence.

2. Geometric Sequence: A geometric sequence has a constant ratio between consecutive terms. We can quickly see that the ratios are not constant since:

   • The ratio of the first two terms is 4 / 9 (not a simple, consistent ratio).
   • Hence, it is not a geometric sequence.

Based on the above examination, the correct classification of the sequence 9, 4, −1, −6 is arithmetic sequence.