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.

(1 point)
Statement #
correctly describes the sequence.

Answer 1

To determine which statement correctly describes the sequence 3, 8, 13, 18, ..., we need to analyze the properties of the sequence.

1. **Arithmetic Sequence**: A sequence is arithmetic if the difference between consecutive terms is constant. Let's find the differences:

- 8 - 3 = 5
- 13 - 8 = 5
- 18 - 13 = 5

The difference between consecutive terms is 5, which is constant. Therefore, this sequence is an arithmetic sequence.

2. **Geometric Sequence**: A sequence is geometric if the ratio between consecutive terms is constant. Let's check the ratios:

- 8 / 3 is not equal to 13 / 8 is not equal to 18 / 13.

Since the ratios are not constant, this sequence is not geometric.

Based on the analysis:

- **Statement #1**: It is an arithmetic sequence. (True)
- **Statement #2**: It is a geometric sequence. (False)

Thus, **Statement #1** correctly describes the sequence.

So the answer is:
Statement #1 correctly describes the sequence.