We appreciate your visit to Sort the sequences according to whether they are arithmetic geometric or neither 1 tex 98 3 94 1 89 9 85 7 ldots tex 2. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To sort the sequences as arithmetic, geometric, or neither, we need to analyze the pattern of numbers in each sequence. Here's how we can do this:
1. Sequence 1: [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex]
- Arithmetic sequence check: Look for a common difference. Calculate the differences 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]
The differences are the same, so this sequence is arithmetic.
2. Sequence 2: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- This sequence alternates between 1, 0, and -1, then back to 0, showing no consistent pattern of addition or multiplication.
- Therefore, this is neither arithmetic nor geometric.
3. Sequence 3: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- Geometric sequence check: Look for a common ratio. Calculate the ratios of consecutive terms:
[tex]\(\frac{3.5}{1.75} = 2\)[/tex]
[tex]\(\frac{7}{3.5} = 2\)[/tex]
[tex]\(\frac{14}{7} = 2\)[/tex]
The ratios are the same, so this sequence is geometric.
4. Sequence 4: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- Arithmetic sequence check: Look for a common difference. Calculate the differences between consecutive terms:
[tex]\(-10.8 - (-12) = 1.2\)[/tex]
[tex]\(-9.6 - (-10.8) = 1.2\)[/tex]
[tex]\(-8.4 - (-9.6) = 1.2\)[/tex]
The differences are the same, so this sequence is arithmetic.
5. Sequence 5: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- This sequence oscillates between -1 and 1. It does not have a consistent pattern of addition or multiplication.
- Therefore, this is neither arithmetic nor geometric.
Based on the analysis:
- Sequence 1 is arithmetic.
- Sequence 2 is neither.
- Sequence 3 is geometric.
- Sequence 4 is arithmetic.
- Sequence 5 is neither.
1. Sequence 1: [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex]
- Arithmetic sequence check: Look for a common difference. Calculate the differences 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]
The differences are the same, so this sequence is arithmetic.
2. Sequence 2: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- This sequence alternates between 1, 0, and -1, then back to 0, showing no consistent pattern of addition or multiplication.
- Therefore, this is neither arithmetic nor geometric.
3. Sequence 3: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- Geometric sequence check: Look for a common ratio. Calculate the ratios of consecutive terms:
[tex]\(\frac{3.5}{1.75} = 2\)[/tex]
[tex]\(\frac{7}{3.5} = 2\)[/tex]
[tex]\(\frac{14}{7} = 2\)[/tex]
The ratios are the same, so this sequence is geometric.
4. Sequence 4: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- Arithmetic sequence check: Look for a common difference. Calculate the differences between consecutive terms:
[tex]\(-10.8 - (-12) = 1.2\)[/tex]
[tex]\(-9.6 - (-10.8) = 1.2\)[/tex]
[tex]\(-8.4 - (-9.6) = 1.2\)[/tex]
The differences are the same, so this sequence is arithmetic.
5. Sequence 5: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- This sequence oscillates between -1 and 1. It does not have a consistent pattern of addition or multiplication.
- Therefore, this is neither arithmetic nor geometric.
Based on the analysis:
- Sequence 1 is arithmetic.
- Sequence 2 is neither.
- Sequence 3 is geometric.
- Sequence 4 is arithmetic.
- Sequence 5 is neither.
Thanks for taking the time to read Sort the sequences according to whether they are arithmetic geometric or neither 1 tex 98 3 94 1 89 9 85 7 ldots tex 2. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
