To analyze the sequence 3, 8, 13, 18, ... we need to look at the differences between consecutive terms to determine whether it is arithmetic or geometric.
- Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant. Let's calculate the differences:
- 8 - 3 = 5
- 13 - 8 = 5
- 18 - 13 = 5
The difference is constant (5) between consecutive terms, which means this sequence is indeed an arithmetic sequence.
- Geometric Sequence: In a geometric sequence, the ratio of consecutive terms is constant. Let's check the ratios:
- 8 / 3 ≈ 2.67
- 13 / 8 = 1.625
- 18 / 13 ≈ 1.385
The ratios are not constant, which means this sequence is not a geometric sequence.
Based on this analysis:
- Statement #1: It is an arithmetic sequence. (True)
- Statement #2: It is a geometric sequence. (False)
Thus, the correct description is that the sequence is an arithmetic sequence.
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