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Answer :
Sure! Let's determine the type of each sequence step-by-step:
1. Sequence 1: [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex]
- To check if it's an arithmetic sequence, we find the difference between consecutive terms:
- [tex]\(94.1 - 98.3 = -4.2\)[/tex]
- [tex]\(89.9 - 94.1 = -4.2\)[/tex]
- [tex]\(85.7 - 89.9 = -4.2\)[/tex]
Since the difference is consistent, this sequence is arithmetic.
2. Sequence 2: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- This sequence has no common difference (varying between 1, 0, -1), nor does it have a common ratio, as division by zero occurs.
This sequence is neither arithmetic nor geometric.
3. Sequence 3: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- To check if it's a geometric sequence, we find the ratio of consecutive terms:
- [tex]\(3.5 / 1.75 = 2\)[/tex]
- [tex]\(7 / 3.5 = 2\)[/tex]
- [tex]\(14 / 7 = 2\)[/tex]
Since the ratio is consistent, this sequence is geometric.
4. Sequence 4: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- To check for an arithmetic sequence, we calculate the difference:
- [tex]\(-10.8 - (-12) = 1.2\)[/tex]
- [tex]\(-9.6 - (-10.8) = 1.2\)[/tex]
- [tex]\(-8.4 - (-9.6) = 1.2\)[/tex]
Since the difference is consistent, this sequence is arithmetic.
5. Sequence 5: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- This sequence alternates between -1 and 1. It doesn't have a common difference or a consistent common ratio because the sign changes.
This sequence is neither arithmetic nor geometric.
In summary:
- Sequence 1: Arithmetic
- Sequence 2: Neither
- Sequence 3: Geometric
- Sequence 4: Arithmetic
- Sequence 5: Neither
1. Sequence 1: [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex]
- To check if it's an arithmetic sequence, we find the difference between consecutive terms:
- [tex]\(94.1 - 98.3 = -4.2\)[/tex]
- [tex]\(89.9 - 94.1 = -4.2\)[/tex]
- [tex]\(85.7 - 89.9 = -4.2\)[/tex]
Since the difference is consistent, this sequence is arithmetic.
2. Sequence 2: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- This sequence has no common difference (varying between 1, 0, -1), nor does it have a common ratio, as division by zero occurs.
This sequence is neither arithmetic nor geometric.
3. Sequence 3: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- To check if it's a geometric sequence, we find the ratio of consecutive terms:
- [tex]\(3.5 / 1.75 = 2\)[/tex]
- [tex]\(7 / 3.5 = 2\)[/tex]
- [tex]\(14 / 7 = 2\)[/tex]
Since the ratio is consistent, this sequence is geometric.
4. Sequence 4: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- To check for an arithmetic sequence, we calculate the difference:
- [tex]\(-10.8 - (-12) = 1.2\)[/tex]
- [tex]\(-9.6 - (-10.8) = 1.2\)[/tex]
- [tex]\(-8.4 - (-9.6) = 1.2\)[/tex]
Since the difference is consistent, this sequence is arithmetic.
5. Sequence 5: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- This sequence alternates between -1 and 1. It doesn't have a common difference or a consistent common ratio because the sign changes.
This sequence is neither arithmetic nor geometric.
In summary:
- Sequence 1: Arithmetic
- Sequence 2: Neither
- Sequence 3: Geometric
- Sequence 4: Arithmetic
- Sequence 5: Neither
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