To classify the sequence 9, 4, -1, -6, we can check the differences between consecutive terms to see if it's an arithmetic sequence, and we can check the ratios of consecutive terms to see if it's a geometric sequence.
Arithmetic Sequence: An arithmetic sequence is one where the difference between consecutive terms is constant.
- 4 - 9 = -5
- -1 - 4 = -5
- -6 - (-1) = -5
The difference between consecutive terms is consistently -5, so the numbers form an arithmetic sequence.
Geometric Sequence: A geometric sequence is one where the ratio of consecutive terms is constant.
- 4 / 9 ≈ 0.4444
- -1 / 4 = -0.25
- -6 / -1 = 6
The ratios are not constant, so this is not a geometric sequence.
Conclusion: The sequence 9, 4, -1, -6 is classified as Arithmetic.