High School

Sort the sequences according to whether they are arithmetic, geometric, or neither.

| Sequence | Type |
|-----------------------------|------------|
| 98.3, 941, 899, 857 | Arithmetic |
| 1, 0, -1, 0 | Neither |
| 175, 35, 7, 1.4 | Geometric |
| -12, -10.8, -9.6, -8.4 | Arithmetic |
| -1, 1, -1, 1 | Neither |

Answer :

To determine the type of each sequence, we look at the differences or ratios between consecutive terms:

1. Sequence: 98.3, 941, 899, 857
- This sequence is neither arithmetic nor geometric. An arithmetic sequence has a constant difference between terms, and a geometric sequence has a constant ratio. In this case, none of these conditions is met.

2. Sequence: 1, 0, -1, 0
- This sequence is neither arithmetic nor geometric. It repeats a pattern without a constant difference or ratio.

3. Sequence: 175, 35, 7.14
- This sequence is neither arithmetic nor geometric. For an arithmetic sequence, there is no consistent subtraction between terms. For a geometric sequence, there is no consistent multiplication factor.

4. Sequence: -12, -10.8, -9.6, -8.4
- This sequence is neither arithmetic nor geometric. It does not maintain consistent arithmetic differences or geometric ratios.

5. Sequence: -1, 1, -1, 1
- This sequence is geometric. It alternates consistently, and the ratio between consecutive terms is -1, indicating a geometric pattern.

Summary:
- The sequence -1, 1, -1, 1 is geometric.
- All other sequences are neither arithmetic nor geometric.