To classify the given sequence \( 9, 4, -1, -6, \ldots \), we need to examine the differences or ratios between the terms to determine the type of sequence.
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Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant. Let's calculate the differences:
- \( 4 - 9 = -5 \)
- \( -1 - 4 = -5 \)
- \( -6 - (-1) = -5 \)
Since the difference is consistent at \(-5\), this sequence is indeed an arithmetic sequence.
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Geometric Sequence: In a geometric sequence, the ratio between consecutive terms is constant. Let's check the ratios:
- \( \frac{4}{9} \)
- \( \frac{-1}{4} \)
- \( \frac{-6}{-1} = 6 \)
The ratios are not constant, which eliminates it being a geometric sequence.
Since the sequence has a constant difference, we classify it as an arithmetic sequence.
Therefore, the answer is:
arithmetic sequence