Answer :
Let's analyze each sequence one by one and determine whether they are arithmetic, geometric, or neither.
1. Sequence: 98.3, 94.1, 89.9, 85.7, ...
- To check if the sequence is arithmetic, we look for a common difference between consecutive terms.
- The difference between each term is [tex]\(94.1 - 98.3 = -4.2\)[/tex], [tex]\(89.9 - 94.1 = -4.2\)[/tex], and [tex]\(85.7 - 89.9 = -4.2\)[/tex].
- Since the difference is constant, this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0, ...
- For arithmetic, the difference between consecutive terms should be constant.
- For geometric, each term should be obtained by multiplying the previous one by a constant factor.
- The differences are not constant, and there is no constant multiplier.
- Thus, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
- For this sequence, we need to check for a common ratio between terms, which would make it geometric.
- The ratio of successive terms is [tex]\(3.5 / 1.75 = 2\)[/tex], [tex]\(7 / 3.5 = 2\)[/tex], and [tex]\(14 / 7 = 2\)[/tex].
- Since there is a common ratio of 2, this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
- Check if there's a common difference for arithmetic progressions.
- The differences are [tex]\(-10.8 - (-12) = 1.2\)[/tex], [tex]\(-9.6 - (-10.8) = 1.2\)[/tex], and [tex]\(-8.4 - (-9.6) = 1.2\)[/tex].
- Since the difference is constant, this sequence is arithmetic.
5. Sequence: -1, 1, -1, 1, ...
- Again, check for arithmetic by finding a common difference or geometric progression with a common ratio.
- This sequence alternates between the same two numbers, neither with a constant difference nor a ratio.
- This sequence is neither arithmetic nor geometric.
So, the classifications are as follows:
- The first sequence is arithmetic.
- The second sequence is neither arithmetic nor geometric.
- The third sequence is geometric.
- The fourth sequence is arithmetic.
- The fifth sequence is neither arithmetic nor geometric.
1. Sequence: 98.3, 94.1, 89.9, 85.7, ...
- To check if the sequence is arithmetic, we look for a common difference between consecutive terms.
- The difference between each term is [tex]\(94.1 - 98.3 = -4.2\)[/tex], [tex]\(89.9 - 94.1 = -4.2\)[/tex], and [tex]\(85.7 - 89.9 = -4.2\)[/tex].
- Since the difference is constant, this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0, ...
- For arithmetic, the difference between consecutive terms should be constant.
- For geometric, each term should be obtained by multiplying the previous one by a constant factor.
- The differences are not constant, and there is no constant multiplier.
- Thus, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
- For this sequence, we need to check for a common ratio between terms, which would make it geometric.
- The ratio of successive terms is [tex]\(3.5 / 1.75 = 2\)[/tex], [tex]\(7 / 3.5 = 2\)[/tex], and [tex]\(14 / 7 = 2\)[/tex].
- Since there is a common ratio of 2, this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
- Check if there's a common difference for arithmetic progressions.
- The differences are [tex]\(-10.8 - (-12) = 1.2\)[/tex], [tex]\(-9.6 - (-10.8) = 1.2\)[/tex], and [tex]\(-8.4 - (-9.6) = 1.2\)[/tex].
- Since the difference is constant, this sequence is arithmetic.
5. Sequence: -1, 1, -1, 1, ...
- Again, check for arithmetic by finding a common difference or geometric progression with a common ratio.
- This sequence alternates between the same two numbers, neither with a constant difference nor a ratio.
- This sequence is neither arithmetic nor geometric.
So, the classifications are as follows:
- The first sequence is arithmetic.
- The second sequence is neither arithmetic nor geometric.
- The third sequence is geometric.
- The fourth sequence is arithmetic.
- The fifth sequence is neither arithmetic nor geometric.
