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Answer :
Let's analyze each sequence to determine whether it is arithmetic, geometric, or neither.
1. Sequence: [tex]\(98.3, 94.1, 89.8, 85.7, \ldots\)[/tex]
- Arithmetic Sequence: This type involves a constant difference between consecutive terms. Let's check the differences:
- Difference: [tex]\(94.1 - 98.3 = -4.2\)[/tex]
- Difference: [tex]\(89.8 - 94.1 = -4.3\)[/tex] (approximately)
- Since the differences are not the same, this is not an arithmetic sequence.
- Geometric Sequence: This type involves a constant ratio between consecutive terms, but since the terms do not have a consistent difference, it is also not geometric.
- Conclusion: This sequence is neither arithmetic nor geometric.
2. Sequence: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- This sequence fluctuates between 1 and -1 and repeats regularly.
- Arithmetic Sequence: No constant difference, so it's not arithmetic.
- Geometric Sequence: No constant ratio, so it's not geometric.
- Conclusion: This sequence is neither arithmetic nor geometric.
3. Sequence: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- Geometric Sequence: Check the ratio between consecutive terms:
- Ratio: [tex]\(3.5 \div 1.75 = 2\)[/tex]
- Ratio: [tex]\(7 \div 3.5 = 2\)[/tex]
- Ratio: [tex]\(14 \div 7 = 2\)[/tex]
- Since the ratio is constant, this is a geometric sequence.
- Conclusion: This sequence is geometric.
4. Sequence: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- Arithmetic Sequence: Check the difference between consecutive terms:
- Difference: [tex]\(-10.8 - (-12) = 1.2\)[/tex]
- Difference: [tex]\(-9.6 - (-10.8) = 1.2\)[/tex]
- Difference: [tex]\(-8.4 - (-9.6) = 1.2\)[/tex]
- Since the difference is constant, this is an arithmetic sequence.
- Conclusion: This sequence is arithmetic.
5. Sequence: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- This is a repeating pattern between -1 and 1.
- Arithmetic Sequence: No constant difference, so it's not arithmetic.
- Geometric Sequence: No constant ratio, so it's not geometric.
- Conclusion: This sequence is neither arithmetic nor geometric.
Based on the analysis, the sequences are classified as follows:
- [tex]\(98.3, 94.1, 89.8, 85.7, \ldots\)[/tex] is neither.
- [tex]\(1, 0, -1, 0, \ldots\)[/tex] is neither.
- [tex]\(1.75, 3.5, 7, 14\)[/tex] is geometric.
- [tex]\(-12, -10.8, -9.6, -8.4\)[/tex] is arithmetic.
- [tex]\(-1, 1, -1, 1, \ldots\)[/tex] is neither.
1. Sequence: [tex]\(98.3, 94.1, 89.8, 85.7, \ldots\)[/tex]
- Arithmetic Sequence: This type involves a constant difference between consecutive terms. Let's check the differences:
- Difference: [tex]\(94.1 - 98.3 = -4.2\)[/tex]
- Difference: [tex]\(89.8 - 94.1 = -4.3\)[/tex] (approximately)
- Since the differences are not the same, this is not an arithmetic sequence.
- Geometric Sequence: This type involves a constant ratio between consecutive terms, but since the terms do not have a consistent difference, it is also not geometric.
- Conclusion: This sequence is neither arithmetic nor geometric.
2. Sequence: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- This sequence fluctuates between 1 and -1 and repeats regularly.
- Arithmetic Sequence: No constant difference, so it's not arithmetic.
- Geometric Sequence: No constant ratio, so it's not geometric.
- Conclusion: This sequence is neither arithmetic nor geometric.
3. Sequence: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- Geometric Sequence: Check the ratio between consecutive terms:
- Ratio: [tex]\(3.5 \div 1.75 = 2\)[/tex]
- Ratio: [tex]\(7 \div 3.5 = 2\)[/tex]
- Ratio: [tex]\(14 \div 7 = 2\)[/tex]
- Since the ratio is constant, this is a geometric sequence.
- Conclusion: This sequence is geometric.
4. Sequence: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- Arithmetic Sequence: Check the difference between consecutive terms:
- Difference: [tex]\(-10.8 - (-12) = 1.2\)[/tex]
- Difference: [tex]\(-9.6 - (-10.8) = 1.2\)[/tex]
- Difference: [tex]\(-8.4 - (-9.6) = 1.2\)[/tex]
- Since the difference is constant, this is an arithmetic sequence.
- Conclusion: This sequence is arithmetic.
5. Sequence: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- This is a repeating pattern between -1 and 1.
- Arithmetic Sequence: No constant difference, so it's not arithmetic.
- Geometric Sequence: No constant ratio, so it's not geometric.
- Conclusion: This sequence is neither arithmetic nor geometric.
Based on the analysis, the sequences are classified as follows:
- [tex]\(98.3, 94.1, 89.8, 85.7, \ldots\)[/tex] is neither.
- [tex]\(1, 0, -1, 0, \ldots\)[/tex] is neither.
- [tex]\(1.75, 3.5, 7, 14\)[/tex] is geometric.
- [tex]\(-12, -10.8, -9.6, -8.4\)[/tex] is arithmetic.
- [tex]\(-1, 1, -1, 1, \ldots\)[/tex] is neither.
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