Answer :
Sure! Let's take a closer look at each sequence and determine whether they are arithmetic, geometric, or neither.
1. Sequence: 98.3, 94.1, 89.9, 85.7
- An arithmetic sequence has a common difference between consecutive terms. To check this, subtract each term from the next one.
- Differences: 94.1 - 98.3 = -4.2, 89.9 - 94.1 = -4.2, 85.7 - 89.9 = -4.2.
- Since the differences are all the same, this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0
- Check for arithmetic: 0 - 1 = -1, -1 - 0 = -1, 0 - (-1) = 1. The differences are not the same.
- Check for geometric: A geometric sequence has a common ratio obtained by dividing each term by the previous term. However, you cannot divide by zero, so this sequence is not geometric either.
- Since neither condition fits, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
- Check for arithmetic: 3.5 - 1.75 = 1.75, 7 - 3.5 = 3.5, 14 - 7 = 7. The differences are not the same.
- Check for geometric: 3.5 / 1.75 = 2, 7 / 3.5 = 2, 14 / 7 = 2. Since each ratio is the same, this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
- Check for arithmetic: -10.8 - (-12) = 1.2, -9.6 - (-10.8) = 1.2, -8.4 - (-9.6) = 1.2. All differences are the same.
- This sequence is arithmetic.
5. Sequence: -1, 1, -1, 1
- This sequence switches between -1 and 1, and doesn't fit the pattern for arithmetic since 1 - (-1) = 2 and -1 - 1 = -2.
- Check for geometric: 1 / -1 = -1 and -1 / 1 = -1, showing a common ratio.
- The sequence is geometric.
To summarize:
- 98.3, 94.1, 89.9, 85.7 is Arithmetic.
- 1, 0, -1, 0 is Neither.
- 1.75, 3.5, 7, 14 is Geometric.
- -12, -10.8, -9.6, -8.4 is Arithmetic.
- -1, 1, -1, 1 is Geometric.
1. Sequence: 98.3, 94.1, 89.9, 85.7
- An arithmetic sequence has a common difference between consecutive terms. To check this, subtract each term from the next one.
- Differences: 94.1 - 98.3 = -4.2, 89.9 - 94.1 = -4.2, 85.7 - 89.9 = -4.2.
- Since the differences are all the same, this sequence is arithmetic.
2. Sequence: 1, 0, -1, 0
- Check for arithmetic: 0 - 1 = -1, -1 - 0 = -1, 0 - (-1) = 1. The differences are not the same.
- Check for geometric: A geometric sequence has a common ratio obtained by dividing each term by the previous term. However, you cannot divide by zero, so this sequence is not geometric either.
- Since neither condition fits, this sequence is neither arithmetic nor geometric.
3. Sequence: 1.75, 3.5, 7, 14
- Check for arithmetic: 3.5 - 1.75 = 1.75, 7 - 3.5 = 3.5, 14 - 7 = 7. The differences are not the same.
- Check for geometric: 3.5 / 1.75 = 2, 7 / 3.5 = 2, 14 / 7 = 2. Since each ratio is the same, this sequence is geometric.
4. Sequence: -12, -10.8, -9.6, -8.4
- Check for arithmetic: -10.8 - (-12) = 1.2, -9.6 - (-10.8) = 1.2, -8.4 - (-9.6) = 1.2. All differences are the same.
- This sequence is arithmetic.
5. Sequence: -1, 1, -1, 1
- This sequence switches between -1 and 1, and doesn't fit the pattern for arithmetic since 1 - (-1) = 2 and -1 - 1 = -2.
- Check for geometric: 1 / -1 = -1 and -1 / 1 = -1, showing a common ratio.
- The sequence is geometric.
To summarize:
- 98.3, 94.1, 89.9, 85.7 is Arithmetic.
- 1, 0, -1, 0 is Neither.
- 1.75, 3.5, 7, 14 is Geometric.
- -12, -10.8, -9.6, -8.4 is Arithmetic.
- -1, 1, -1, 1 is Geometric.
