Answer :
Sure! Let's go through each of the sequences and determine whether they are arithmetic, geometric, or neither.
1. Sequence: 1, 0, -1, 0, ...
- To determine if it's arithmetic, check for a constant difference between consecutive terms. Here, the differences are: 0 - 1 = -1, -1 - 0 = -1, 0 - (-1) = 1. The differences are not constant.
- For a geometric sequence, the ratio between consecutive terms must be constant. Here, the ratios are: 0/1 is not defined, (-1/0) is not defined. The ratios are not constant.
Conclusion: This sequence is neither arithmetic nor geometric.
2. Sequence: 1.75, 35, 7, 14
- Check for arithmetic by looking at the differences: 35 - 1.75 = 33.25, 7 - 35 = -28, 14 - 7 = 7. The differences are not constant.
- Check for geometric by examining the ratios: 35/1.75, 7/35, 14/7 are 20, 0.2, and 2. The ratios are not constant.
Conclusion: This sequence is neither arithmetic nor geometric.
3. Sequence: -1, 1, -1, 1
- Constant differences for arithmetic are not present: 1 - (-1) = 2, -1 - 1 = -2, 1 - (-1) = 2. They alternate.
- Ratios for geometric sequence are also alternating: 1/(-1) = -1, (-1)/1 = -1, 1/(-1) = -1.
Conclusion: This sequence is neither arithmetic nor geometric.
4. Sequence: 98.3, 94.1, 89.9, 85.7, ...
- Check for a constant difference: 94.1 - 98.3 = -4.2, 89.9 - 94.1 = -4.2, 85.7 - 89.9 = -4.2. The differences are constant.
Conclusion: This sequence is arithmetic.
5. Sequence: -12, -10.8, -9.6, -8.4
- Look for a constant difference: -10.8 - (-12) = 1.2, -9.6 - (-10.8) = 1.2, -8.4 - (-9.6) = 1.2. The differences are constant.
Conclusion: This sequence is arithmetic.
So, the final categorization for the sequences is:
- 1st Sequence: Neither
- 2nd Sequence: Neither
- 3rd Sequence: Neither
- 4th Sequence: Arithmetic
- 5th Sequence: Arithmetic
1. Sequence: 1, 0, -1, 0, ...
- To determine if it's arithmetic, check for a constant difference between consecutive terms. Here, the differences are: 0 - 1 = -1, -1 - 0 = -1, 0 - (-1) = 1. The differences are not constant.
- For a geometric sequence, the ratio between consecutive terms must be constant. Here, the ratios are: 0/1 is not defined, (-1/0) is not defined. The ratios are not constant.
Conclusion: This sequence is neither arithmetic nor geometric.
2. Sequence: 1.75, 35, 7, 14
- Check for arithmetic by looking at the differences: 35 - 1.75 = 33.25, 7 - 35 = -28, 14 - 7 = 7. The differences are not constant.
- Check for geometric by examining the ratios: 35/1.75, 7/35, 14/7 are 20, 0.2, and 2. The ratios are not constant.
Conclusion: This sequence is neither arithmetic nor geometric.
3. Sequence: -1, 1, -1, 1
- Constant differences for arithmetic are not present: 1 - (-1) = 2, -1 - 1 = -2, 1 - (-1) = 2. They alternate.
- Ratios for geometric sequence are also alternating: 1/(-1) = -1, (-1)/1 = -1, 1/(-1) = -1.
Conclusion: This sequence is neither arithmetic nor geometric.
4. Sequence: 98.3, 94.1, 89.9, 85.7, ...
- Check for a constant difference: 94.1 - 98.3 = -4.2, 89.9 - 94.1 = -4.2, 85.7 - 89.9 = -4.2. The differences are constant.
Conclusion: This sequence is arithmetic.
5. Sequence: -12, -10.8, -9.6, -8.4
- Look for a constant difference: -10.8 - (-12) = 1.2, -9.6 - (-10.8) = 1.2, -8.4 - (-9.6) = 1.2. The differences are constant.
Conclusion: This sequence is arithmetic.
So, the final categorization for the sequences is:
- 1st Sequence: Neither
- 2nd Sequence: Neither
- 3rd Sequence: Neither
- 4th Sequence: Arithmetic
- 5th Sequence: Arithmetic
