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

1. Arithmetic Sequences:
- [tex]$98.3, 94.1, 89.9, 85.7, \ldots$[/tex]
- [tex]$-12, -10.8, -9.6, -8.4$[/tex]

2. Geometric Sequences:
- [tex]$1.75, 3.5, 7, 14$[/tex]

3. Neither Arithmetic nor Geometric:
- [tex]$1, 0, -1, 0, \ldots$[/tex]
- [tex]$-1, 1, -1, 1, \ldots$[/tex]

Answer :

Let's classify each sequence as arithmetic, geometric, or neither:

1. Sequence: 98.3, 94.1, 89.9, 85.7,...
- To determine if a sequence is arithmetic, we check if the difference between consecutive terms is constant.
- Look at the differences:
- Difference between 94.1 and 98.3: 94.1 - 98.3 = -4.2
- Difference between 89.9 and 94.1: 89.9 - 94.1 = -4.2
- Difference between 85.7 and 89.9: 85.7 - 89.9 = -4.2
- All differences are the same, so this sequence is arithmetic.

2. Sequence: 1, 0, -1, 0,...
- This sequence alternates and does not have a constant difference or ratio, so it is neither arithmetic nor geometric.

3. Sequence: 1.75, 3.5, 7, 14
- To determine if a sequence is geometric, we check if the ratio between consecutive terms is constant.
- Look at the ratios:
- Ratio between 3.5 and 1.75: 3.5 / 1.75 = 2
- Ratio between 7 and 3.5: 7 / 3.5 = 2
- Ratio between 14 and 7: 14 / 7 = 2
- All ratios are the same, so this sequence is geometric.

4. Sequence: -12, -10.8, -9.6, -8.4
- Look at the differences:
- Difference between -10.8 and -12: -10.8 - (-12) = 1.2
- Difference between -9.6 and -10.8: -9.6 - (-10.8) = 1.2
- Difference between -8.4 and -9.6: -8.4 - (-9.6) = 1.2
- All differences are the same, so this sequence is arithmetic.

5. Sequence: -1, 1, -1, 1,...
- This sequence alternates and does not have a constant difference or ratio, so it is neither arithmetic nor geometric.

In summary:
- Sequence 1 is arithmetic.
- Sequence 2 is neither.
- Sequence 3 is geometric.
- Sequence 4 is arithmetic.
- Sequence 5 is neither.

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