Answer :
Let's classify each sequence as arithmetic, geometric, or neither using a step-by-step approach:
1. First Sequence: 98.3, 94.1, 89.9, 85.7, ...
- Check for arithmetic: Calculate the differences between successive terms.
- 94.1 - 98.3 = -4.2
- 89.9 - 94.1 = -4.2
- 85.7 - 89.9 = -4.2
- The differences are consistent, so this is an arithmetic sequence with a common difference of -4.2.
2. Second Sequence: 1, 0, -1, 0, ...
- Check for arithmetic: Differences between terms are not consistent.
- 0 - 1 = -1
- (-1) - 0 = -1
- 0 - (-1) = 1
- Check for geometric: Ratios between terms are undefined or not consistent (dividing by zero).
- Since it's neither arithmetic nor geometric, this sequence is neither.
3. Third Sequence: 1.75, 3.5, 7, 14, ...
- Check for geometric: Calculate the ratios between successive terms.
- 3.5 / 1.75 = 2
- 7 / 3.5 = 2
- 14 / 7 = 2
- The ratios are consistent, so this is a geometric sequence with a common ratio of 2.
4. Fourth Sequence: -12, -10.8, -9.6, -8.4, ...
- Check for arithmetic: Calculate the differences between successive terms.
- -10.8 - (-12) = 1.2
- -9.6 - (-10.8) = 1.2
- -8.4 - (-9.6) = 1.2
- The differences are consistent, so this is an arithmetic sequence with a common difference of 1.2.
5. Fifth Sequence: -1, 1, -1, 1, ...
- Check for alternating pattern: The sequence oscillates between -1 and 1.
- Neither arithmetic (differences: 2, -2, 2, ...) nor geometric (ratios: -1, -1, ...) due to inconsistent values.
- Therefore, this sequence is neither.
Based on the above analysis, we classify the sequences as follows:
- First Sequence: Arithmetic
- Second Sequence: Neither
- Third Sequence: Geometric
- Fourth Sequence: Arithmetic
- Fifth Sequence: Neither
1. First Sequence: 98.3, 94.1, 89.9, 85.7, ...
- Check for arithmetic: Calculate the differences between successive terms.
- 94.1 - 98.3 = -4.2
- 89.9 - 94.1 = -4.2
- 85.7 - 89.9 = -4.2
- The differences are consistent, so this is an arithmetic sequence with a common difference of -4.2.
2. Second Sequence: 1, 0, -1, 0, ...
- Check for arithmetic: Differences between terms are not consistent.
- 0 - 1 = -1
- (-1) - 0 = -1
- 0 - (-1) = 1
- Check for geometric: Ratios between terms are undefined or not consistent (dividing by zero).
- Since it's neither arithmetic nor geometric, this sequence is neither.
3. Third Sequence: 1.75, 3.5, 7, 14, ...
- Check for geometric: Calculate the ratios between successive terms.
- 3.5 / 1.75 = 2
- 7 / 3.5 = 2
- 14 / 7 = 2
- The ratios are consistent, so this is a geometric sequence with a common ratio of 2.
4. Fourth Sequence: -12, -10.8, -9.6, -8.4, ...
- Check for arithmetic: Calculate the differences between successive terms.
- -10.8 - (-12) = 1.2
- -9.6 - (-10.8) = 1.2
- -8.4 - (-9.6) = 1.2
- The differences are consistent, so this is an arithmetic sequence with a common difference of 1.2.
5. Fifth Sequence: -1, 1, -1, 1, ...
- Check for alternating pattern: The sequence oscillates between -1 and 1.
- Neither arithmetic (differences: 2, -2, 2, ...) nor geometric (ratios: -1, -1, ...) due to inconsistent values.
- Therefore, this sequence is neither.
Based on the above analysis, we classify the sequences as follows:
- First Sequence: Arithmetic
- Second Sequence: Neither
- Third Sequence: Geometric
- Fourth Sequence: Arithmetic
- Fifth Sequence: Neither
