Use the graph below to determine a, and d for the sequence. {(1, 17), (2, 14), (3, 11), (4, 8), (6,5), (6,2)) 20 18 · -16+ -14 + -12 -10 8 4+ 2 Oa₁ = 1; d = 3 Oa₁ = 1; d = -3 Oa₁ = 17; d = 3 Oa₁ =17; d = -3
Use the graph below to determine a, and d for the sequence. {(1, 17), (2, 14), (3, 11), (4, 8), (6,5), (6,2)) 20 18 · -16+ -14 + -12 -10 8 4+ 2 Oa₁ = 1; d = 3 Oa₁ = 1; d = -3 Oa₁ = 17; d = 3 Oa₁ =17; d = -3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Determining the First Term \(a_1\) and Common Difference \(d\) of the Sequence
#### Introduction
The task is to use the provided graph to identify the first term \(a_1\) and the common difference \(d\) for an arithmetic sequence.
#### Graph Analysis
The graph plots a set of points:
- \( (1, 17) \)
- \( (2, 14) \)
- \( (3, 11) \)
- \( (4, 8) \)
- \( (5, 5) \)
- \( (6, 2) \)
Each point suggests the term in the sequence at a specific position \(n\).
#### Sequence Patterns
Depending on the coordinates of each point:
- The first point is at \( (1, 17) \), suggesting \( a_1 = 17 \).
- The second point is at \( (2, 14) \), giving \( a_2 = 14 \) and suggesting the common difference \(d\).
To find \(d\), calculate the difference between any two successive terms:
\[ d = 14 - 17 = -3 \]
The subsequent points confirm this common difference \(d\).
- \( (3, 11) \): \( 11 - 14 = -3 \)
- \( (4, 8) \): \( 8 - 11 = -3 \)
- And so on.
#### Conclusion
Thus, the first term \(a_1\) is 17 and the common difference \(d\) is -3.
#### Multiple Choice Question
Choose the correct values for \(a_1\) and \(d\) from the options provided:
- \(a_1 = 1; d = 3\)
- \(a_1 = 1; d = -3\)
- \(a_1 = 17; d = 3\)
- **\(a_1 = 17; d = -3\)** (Correct Answer)
This analysis helps in understanding how to determine the first term and the common difference of an arithmetic sequence using a graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F355372c0-0b06-4568-8d9a-cddd4364f7ea%2F0df24659-942e-49f9-8925-8c62dcc3df0b%2F7cn949j_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the First Term \(a_1\) and Common Difference \(d\) of the Sequence
#### Introduction
The task is to use the provided graph to identify the first term \(a_1\) and the common difference \(d\) for an arithmetic sequence.
#### Graph Analysis
The graph plots a set of points:
- \( (1, 17) \)
- \( (2, 14) \)
- \( (3, 11) \)
- \( (4, 8) \)
- \( (5, 5) \)
- \( (6, 2) \)
Each point suggests the term in the sequence at a specific position \(n\).
#### Sequence Patterns
Depending on the coordinates of each point:
- The first point is at \( (1, 17) \), suggesting \( a_1 = 17 \).
- The second point is at \( (2, 14) \), giving \( a_2 = 14 \) and suggesting the common difference \(d\).
To find \(d\), calculate the difference between any two successive terms:
\[ d = 14 - 17 = -3 \]
The subsequent points confirm this common difference \(d\).
- \( (3, 11) \): \( 11 - 14 = -3 \)
- \( (4, 8) \): \( 8 - 11 = -3 \)
- And so on.
#### Conclusion
Thus, the first term \(a_1\) is 17 and the common difference \(d\) is -3.
#### Multiple Choice Question
Choose the correct values for \(a_1\) and \(d\) from the options provided:
- \(a_1 = 1; d = 3\)
- \(a_1 = 1; d = -3\)
- \(a_1 = 17; d = 3\)
- **\(a_1 = 17; d = -3\)** (Correct Answer)
This analysis helps in understanding how to determine the first term and the common difference of an arithmetic sequence using a graph.
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