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

not a sequence
not a sequence

arithmetic sequence
arithmetic sequence

geometric sequence
geometric sequence

some other sequence

Answer 1

To determine whether the sequence 9, 4, −1, −6, ... is arithmetic, geometric, or some other type, we can analyze the differences and ratios between consecutive terms.

1. Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant.
   • Difference between terms:
     • \( 4 - 9 = -5 \)
     • \( -1 - 4 = -5 \)
     • \( -6 - (-1) = -5 \)
   • The difference is the same (-5) for all pairs of consecutive terms.

Since the difference is constant, we can conclude that this sequence is an arithmetic sequence.

Thus, the answer is: arithmetic sequence