Answer :
Sure! Let's go through each sequence step-by-step to determine whether they are arithmetic, geometric, or neither.
1. Sequence 1: 98.3, 94.1, 89.9, 85.7, ...
- Arithmetic Check: In an arithmetic sequence, each term increases or decreases by a constant difference. Let's find the differences:
- 94.1 - 98.3 = -4.2
- 89.9 - 94.1 = -4.2
Since the differences are constant (-4.2), this sequence is arithmetic.
2. Sequence 2: 1, 0, -1, 0, ...
- Arithmetic Check: Let's determine the differences:
- 0 - 1 = -1
- -1 - 0 = -1
Although two consecutive differences are the same (-1), the sequence pattern restarts making it neither arithmetic nor geometric over extended terms.
- Conclusion: This sequence is neither arithmetic nor geometric.
3. Sequence 3: 1.75, 3.5, 7, 14
- Geometric Check: In a geometric sequence, each term after the first is found by multiplying the previous one by a constant (the common ratio):
- 3.5 / 1.75 = 2
- 7 / 3.5 = 2
- 14 / 7 = 2
Each ratio is the same (2), so this sequence is geometric.
4. Sequence 4: -12, -10.8, -9.6, -8.4
- Arithmetic Check: Let's find the differences:
- -10.8 - (-12) = 1.2
- -9.6 - (-10.8) = 1.2
- -8.4 - (-9.6) = 1.2
The constant difference is +1.2, so this sequence is arithmetic.
5. Sequence 5: -1, 1, -1, 1, ...
- Arithmetic Check: Determine the differences:
- 1 - (-1) = 2
- -1 - 1 = -2
The differences alternate, meaning it's not a consistent pattern in the context of arithmetic or geometric sequences.
- Conclusion: This sequence is neither arithmetic nor geometric.
I hope this helps you understand how to identify arithmetic and geometric sequences!
1. Sequence 1: 98.3, 94.1, 89.9, 85.7, ...
- Arithmetic Check: In an arithmetic sequence, each term increases or decreases by a constant difference. Let's find the differences:
- 94.1 - 98.3 = -4.2
- 89.9 - 94.1 = -4.2
Since the differences are constant (-4.2), this sequence is arithmetic.
2. Sequence 2: 1, 0, -1, 0, ...
- Arithmetic Check: Let's determine the differences:
- 0 - 1 = -1
- -1 - 0 = -1
Although two consecutive differences are the same (-1), the sequence pattern restarts making it neither arithmetic nor geometric over extended terms.
- Conclusion: This sequence is neither arithmetic nor geometric.
3. Sequence 3: 1.75, 3.5, 7, 14
- Geometric Check: In a geometric sequence, each term after the first is found by multiplying the previous one by a constant (the common ratio):
- 3.5 / 1.75 = 2
- 7 / 3.5 = 2
- 14 / 7 = 2
Each ratio is the same (2), so this sequence is geometric.
4. Sequence 4: -12, -10.8, -9.6, -8.4
- Arithmetic Check: Let's find the differences:
- -10.8 - (-12) = 1.2
- -9.6 - (-10.8) = 1.2
- -8.4 - (-9.6) = 1.2
The constant difference is +1.2, so this sequence is arithmetic.
5. Sequence 5: -1, 1, -1, 1, ...
- Arithmetic Check: Determine the differences:
- 1 - (-1) = 2
- -1 - 1 = -2
The differences alternate, meaning it's not a consistent pattern in the context of arithmetic or geometric sequences.
- Conclusion: This sequence is neither arithmetic nor geometric.
I hope this helps you understand how to identify arithmetic and geometric sequences!
