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Answer :
Sure, let's analyze each sequence step by step to determine if they are arithmetic, geometric, or neither.
1. Sequence: 98.3, 94.1, 89.9, 85.7
To check if a sequence is arithmetic, the difference between consecutive terms should be constant.
- The difference between 94.1 and 98.3 is 94.1 - 98.3 = -4.2.
- The difference between 89.9 and 94.1 is 89.9 - 94.1 = -4.2.
- The difference between 85.7 and 89.9 is 85.7 - 89.9 = -4.2.
Since the difference is the same, this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0, ...
This sequence alternates between 1, 0, and -1. It does not have a constant difference or a constant ratio.
Therefore, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
To check if a sequence is geometric, the ratio between consecutive terms should be constant.
- The ratio between 3.5 and 1.75 is 3.5 / 1.75 = 2.
- The ratio between 7 and 3.5 is 7 / 3.5 = 2.
- The ratio between 14 and 7 is 14 / 7 = 2.
Since the ratio is the same, this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
Again, check for a constant difference for an arithmetic sequence.
- The difference between -10.8 and -12 is -10.8 - (-12) = 1.2.
- The difference between -9.6 and -10.8 is -9.6 - (-10.8) = 1.2.
- The difference between -8.4 and -9.6 is -8.4 - (-9.6) = 1.2.
Since the difference is consistent, this sequence is arithmetic.
5. Sequence: -1, 1, -1, 1, ...
This sequence is alternating between -1 and 1. It does not have a constant difference or a constant ratio.
Therefore, this sequence is neither arithmetic nor geometric.
To summarize:
- Arithmetic: 98.3, 94.1, 89.9, 85.7 and -12, -10.8, -9.6, -8.4
- Geometric: 1.75, 3.5, 7, 14
- Neither: 1, 0, -1, 0, ... and -1, 1, -1, 1, ...
1. Sequence: 98.3, 94.1, 89.9, 85.7
To check if a sequence is arithmetic, the difference between consecutive terms should be constant.
- The difference between 94.1 and 98.3 is 94.1 - 98.3 = -4.2.
- The difference between 89.9 and 94.1 is 89.9 - 94.1 = -4.2.
- The difference between 85.7 and 89.9 is 85.7 - 89.9 = -4.2.
Since the difference is the same, this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0, ...
This sequence alternates between 1, 0, and -1. It does not have a constant difference or a constant ratio.
Therefore, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
To check if a sequence is geometric, the ratio between consecutive terms should be constant.
- The ratio between 3.5 and 1.75 is 3.5 / 1.75 = 2.
- The ratio between 7 and 3.5 is 7 / 3.5 = 2.
- The ratio between 14 and 7 is 14 / 7 = 2.
Since the ratio is the same, this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
Again, check for a constant difference for an arithmetic sequence.
- The difference between -10.8 and -12 is -10.8 - (-12) = 1.2.
- The difference between -9.6 and -10.8 is -9.6 - (-10.8) = 1.2.
- The difference between -8.4 and -9.6 is -8.4 - (-9.6) = 1.2.
Since the difference is consistent, this sequence is arithmetic.
5. Sequence: -1, 1, -1, 1, ...
This sequence is alternating between -1 and 1. It does not have a constant difference or a constant ratio.
Therefore, this sequence is neither arithmetic nor geometric.
To summarize:
- Arithmetic: 98.3, 94.1, 89.9, 85.7 and -12, -10.8, -9.6, -8.4
- Geometric: 1.75, 3.5, 7, 14
- Neither: 1, 0, -1, 0, ... and -1, 1, -1, 1, ...
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