To determine whether the sequence \(-30, -13, 4\) is arithmetic, geometric, or neither, we first need to analyze the characteristics of each type of sequence.
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Arithmetic Sequence: A sequence is arithmetic if the difference between consecutive terms is constant. We can calculate the differences:
- Difference between second and first term: \(-13 - (-30) = -13 + 30 = 17\)
- Difference between third and second term: \(4 - (-13) = 4 + 13 = 17\)
Since the difference is the same (17), this sequence is an arithmetic sequence.
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Geometric Sequence: A sequence is geometric if the ratio between consecutive terms is constant. We can calculate the ratios:
- Ratio between second and first term: \(-13 / -30 = \frac{13}{30}\)
- Ratio between third and second term: \(4 / -13\)
Since the ratios are not the same, this sequence is not geometric.
Since the sequence has a constant difference between terms, it is classified as an arithmetic sequence.