To determine the classification of the given sequence (9, 4, −1, −6, ...), we need to check if it follows the rules for an arithmetic or a geometric sequence.
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Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant.
Let's find the differences:
- 4 - 9 = -5
- -1 - 4 = -5
- -6 - (-1) = -5
The difference between each pair of consecutive terms is the same (-5), so this is an arithmetic sequence.
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Geometric Sequence: In a geometric sequence, the ratio of consecutive terms is constant.
Let's find the ratios:
- 4 / 9 = 4/9
- -1 / 4 = -1/4
- -6 / -1 = 6
The ratios are not constant, so this is not a geometric sequence.
Therefore, the correct classification of the sequence (9, 4, −1, −6, ...) is:
arithmetic sequence.