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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

Arithmetic
Arithmetic

Not enough information given
Not enough information given

Neither

1 answer

To determine whether the sequence \(9, 4, -1, -6\) is an arithmetic sequence, a geometric sequence, or neither, we need to check the definitions:

  1. Arithmetic Sequence: A sequence where the difference between consecutive terms is constant.
  2. Geometric Sequence: A sequence where the ratio between consecutive terms is constant.

Checking for Arithmetic Sequence:

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

The common difference is \(-5\) for all pairs of consecutive terms, which confirms it is an arithmetic sequence.

Checking for Geometric Sequence:

  • \(\frac{4}{9} \neq \frac{-1}{4} \neq \frac{-6}{-1}\)

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

Since the sequence has a constant difference, it is classified as an Arithmetic sequence.

Final Response: Arithmetic