Question

Which of the following statements correctly describes the sequence 3, 8, 13, 18, . . .?

Statement #1: It is an arithmetic sequence.

Statement #2: It is a geometric sequence

Answer 1

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.

1. **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.

2. **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.