Question

is the sequence geometric or arithmetic?
3, 6, 9, 12..

Answer 1

The given sequence is 3, 6, 9, 12.

To determine if it is arithmetic or geometric, we can look at the differences or ratios between consecutive terms:

1. **Arithmetic sequence**: A sequence is arithmetic if the difference between consecutive terms is constant.
- Differences:
- 6 - 3 = 3
- 9 - 6 = 3
- 12 - 9 = 3
- The common difference is 3, which is constant.

2. **Geometric sequence**: A sequence is geometric if the ratio of consecutive terms is constant.
- Ratios:
- 6 / 3 = 2
- 9 / 6 = 1.5
- 12 / 9 = 1.33 (approx.)
- The ratios are not constant.

Since the sequence has a constant difference of 3, it is an **arithmetic sequence**.