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Classify the following list of numbers as an arithmetic sequence, a geometric sequence, or neither.

9,4,-1,-6

(1 point)
Responses

Geometric
Geometric

Not enough information given
Not enough information given

Arithmetic
Arithmetic

Neither

1 answer

To classify the given sequence \(9, 4, -1, -6\), we need to check if it is an arithmetic sequence or a geometric sequence.

  1. Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant.

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

    Since the difference between every two consecutive terms is the same (-5), this sequence is an arithmetic sequence.

  2. Geometric Sequence: In a geometric sequence, the ratio between consecutive terms is constant.

    • \( \frac{4}{9} \) (not constant with the next ratios)
    • \( \frac{-1}{4} \)
    • \( \frac{-6}{-1} = 6 \)

    The ratios are not the same, so this is not a geometric sequence.

Since the sequence confirms the properties of an arithmetic sequence, the correct response is:

Arithmetic