Answer :
Let's analyze each sequence one by one to determine whether they are arithmetic, geometric, or neither.
1. Sequence: 98.3, 94.1, 89.9, 85.7, ...
- To check if this is an arithmetic sequence, calculate the difference between consecutive terms:
- 94.1 - 98.3 = -4.2
- 89.9 - 94.1 = -4.2
- 85.7 - 89.9 = -4.2
- Since the difference between each term is constant (-4.2), this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0, ...
- Calculate the difference between consecutive terms to check if it's arithmetic:
- 0 - 1 = -1
- -1 - 0 = -1
- 0 - (-1) = 1
- The differences are not constant, so it's not arithmetic.
- For a geometric sequence, check the ratio:
- 0 / 1 = 0
- (-1) / 0 is undefined, so no constant ratio exists.
- Since neither the difference nor the ratio is constant, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
- Calculate the difference between consecutive terms to check if it's arithmetic:
- 3.5 - 1.75 = 1.75
- 7 - 3.5 = 3.5
- 14 - 7 = 7
- The differences are not constant, so it's not arithmetic.
- For a geometric sequence, check the ratio:
- 3.5 / 1.75 = 2
- 7 / 3.5 = 2
- 14 / 7 = 2
- The ratio between each term is constant (2), so this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
- Calculate the difference between consecutive terms:
- -10.8 - (-12) = 1.2
- -9.6 - (-10.8) = 1.2
- -8.4 - (-9.6) = 1.2
- Since the difference between each term is constant (1.2), this sequence is arithmetic.
5. Sequence: -1, 1, -1, 1, ...
- Calculate the difference between consecutive terms:
- 1 - (-1) = 2
- -1 - 1 = -2
- 1 - (-1) = 2
- The differences are not constant, so it's not arithmetic.
- For a geometric sequence, check the ratio:
- 1 / -1 = -1
- -1 / 1 = -1
- 1 / -1 = -1
- Even though the ratios are the same, the sequence alternates, indicating a pattern that's neither strictly arithmetic nor geometric in nature.
So, the sequences are classified as follows:
1. Arithmetic
2. Neither
3. Geometric
4. Arithmetic
5. Neither
1. Sequence: 98.3, 94.1, 89.9, 85.7, ...
- To check if this is an arithmetic sequence, calculate the difference between consecutive terms:
- 94.1 - 98.3 = -4.2
- 89.9 - 94.1 = -4.2
- 85.7 - 89.9 = -4.2
- Since the difference between each term is constant (-4.2), this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0, ...
- Calculate the difference between consecutive terms to check if it's arithmetic:
- 0 - 1 = -1
- -1 - 0 = -1
- 0 - (-1) = 1
- The differences are not constant, so it's not arithmetic.
- For a geometric sequence, check the ratio:
- 0 / 1 = 0
- (-1) / 0 is undefined, so no constant ratio exists.
- Since neither the difference nor the ratio is constant, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
- Calculate the difference between consecutive terms to check if it's arithmetic:
- 3.5 - 1.75 = 1.75
- 7 - 3.5 = 3.5
- 14 - 7 = 7
- The differences are not constant, so it's not arithmetic.
- For a geometric sequence, check the ratio:
- 3.5 / 1.75 = 2
- 7 / 3.5 = 2
- 14 / 7 = 2
- The ratio between each term is constant (2), so this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
- Calculate the difference between consecutive terms:
- -10.8 - (-12) = 1.2
- -9.6 - (-10.8) = 1.2
- -8.4 - (-9.6) = 1.2
- Since the difference between each term is constant (1.2), this sequence is arithmetic.
5. Sequence: -1, 1, -1, 1, ...
- Calculate the difference between consecutive terms:
- 1 - (-1) = 2
- -1 - 1 = -2
- 1 - (-1) = 2
- The differences are not constant, so it's not arithmetic.
- For a geometric sequence, check the ratio:
- 1 / -1 = -1
- -1 / 1 = -1
- 1 / -1 = -1
- Even though the ratios are the same, the sequence alternates, indicating a pattern that's neither strictly arithmetic nor geometric in nature.
So, the sequences are classified as follows:
1. Arithmetic
2. Neither
3. Geometric
4. Arithmetic
5. Neither
