Question

7,12,10,15
is this arithmetic geometric or neither

Answer 1

To determine whether the sequence \(7, 12, 10, 15\) is arithmetic, geometric, or neither, we can analyze its properties.

1. **Arithmetic Sequence**: A sequence is arithmetic if the difference between consecutive terms is constant.

- \(12 - 7 = 5\)
- \(10 - 12 = -2\)
- \(15 - 10 = 5\)

The differences are \(5, -2, 5\), which are not constant. Therefore, the sequence is not arithmetic.

2. **Geometric Sequence**: A sequence is geometric if the ratio between consecutive terms is constant.

- \(12 / 7 \approx 1.714\)
- \(10 / 12 \approx 0.833\)
- \(15 / 10 = 1.5\)

The ratios are approximately \(1.714, 0.833, 1.5\), which are also not constant. Therefore, the sequence is not geometric.

Since the sequence does not exhibit the properties of an arithmetic or geometric sequence, we can conclude that it is **neither**.