Answer :
Certainly! Let's evaluate each sequence to determine whether they are arithmetic, geometric, or neither.
1. Sequence: 98.3, 94.1, 89.9, 85.7, ...
- Arithmetic Check: An arithmetic sequence has a constant difference between consecutive terms. Let's find the differences:
- 94.1 - 98.3 = -4.2
- 89.9 - 94.1 = -4.2
- 85.7 - 89.9 = -4.2
The difference is constant, so this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0, ...
- Arithmetic Check:
- 0 - 1 = -1
- -1 - 0 = -1
- 0 - (-1) = 1
The differences are not constant.
- Geometric Check: A geometric sequence has a constant ratio between consecutive terms.
- 0 / 1 is undefined or 0, and the next ratios will not be consistent.
Thus, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
- Arithmetic Check:
- 3.5 - 1.75 = 1.75
- 7 - 3.5 = 3.5
- 14 - 7 = 7
The differences are not constant.
- Geometric Check:
- 3.5 / 1.75 = 2
- 7 / 3.5 = 2
- 14 / 7 = 2
The ratios are constant, so this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
- Arithmetic Check:
- -10.8 - (-12) = 1.2
- -9.6 - (-10.8) = 1.2
- -8.4 - (-9.6) = 1.2
The difference is constant, so this sequence is arithmetic.
5. Sequence: -1, 1, -1, 1, ...
- Arithmetic Check:
- 1 - (-1) = 2
- -1 - 1 = -2
- 1 - (-1) = 2
The differences are not constant.
- Geometric Check:
- 1 / (-1) = -1
- -1 / 1 = -1
- 1 / (-1) = -1
The ratios are constant, so this sequence is geometric.
In summary:
- Sequence 1: Arithmetic
- Sequence 2: Neither
- Sequence 3: Geometric
- Sequence 4: Arithmetic
- Sequence 5: Geometric
1. Sequence: 98.3, 94.1, 89.9, 85.7, ...
- Arithmetic Check: An arithmetic sequence has a constant difference between consecutive terms. Let's find the differences:
- 94.1 - 98.3 = -4.2
- 89.9 - 94.1 = -4.2
- 85.7 - 89.9 = -4.2
The difference is constant, so this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0, ...
- Arithmetic Check:
- 0 - 1 = -1
- -1 - 0 = -1
- 0 - (-1) = 1
The differences are not constant.
- Geometric Check: A geometric sequence has a constant ratio between consecutive terms.
- 0 / 1 is undefined or 0, and the next ratios will not be consistent.
Thus, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
- Arithmetic Check:
- 3.5 - 1.75 = 1.75
- 7 - 3.5 = 3.5
- 14 - 7 = 7
The differences are not constant.
- Geometric Check:
- 3.5 / 1.75 = 2
- 7 / 3.5 = 2
- 14 / 7 = 2
The ratios are constant, so this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
- Arithmetic Check:
- -10.8 - (-12) = 1.2
- -9.6 - (-10.8) = 1.2
- -8.4 - (-9.6) = 1.2
The difference is constant, so this sequence is arithmetic.
5. Sequence: -1, 1, -1, 1, ...
- Arithmetic Check:
- 1 - (-1) = 2
- -1 - 1 = -2
- 1 - (-1) = 2
The differences are not constant.
- Geometric Check:
- 1 / (-1) = -1
- -1 / 1 = -1
- 1 / (-1) = -1
The ratios are constant, so this sequence is geometric.
In summary:
- Sequence 1: Arithmetic
- Sequence 2: Neither
- Sequence 3: Geometric
- Sequence 4: Arithmetic
- Sequence 5: Geometric
