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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

some other sequence
some other sequence

arithmetic sequence
arithmetic sequence

not a sequence
not a sequence

geometric sequence

1 answer

To classify the sequence \( 9, 4, -1, -6, \ldots \):

  1. Arithmetic sequence: A sequence is arithmetic if there is a constant difference between consecutive terms. For this sequence:

    • \( 4 - 9 = -5 \)
    • \( -1 - 4 = -5 \)
    • \( -6 - (-1) = -5 \)

    Since the difference is consistent at \(-5\), this is an arithmetic sequence.

  2. Geometric sequence: A sequence is geometric if there is a constant ratio between consecutive terms. In this case:

    • \( \frac{4}{9}, \frac{-1}{4}, \frac{-6}{-1} \) are not constant ratios.

Therefore, the correct classification is:

arithmetic sequence.