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18Ty 17 16 15 14 13 12 11 10 8 6 5 4 2 O TY? .(5, 17) (4, 12) (3,7) (2, 2) (1, -3) 12 3 4 5 6 7 8 9 10 11 12 What is the equation for the nth term of the arithmetic sequence

18Ty 17 16 15 14 13 12 11 10 8 6 5 4 2 O TY? .(5, 17) (4, 12) (3,7) (2, 2) (1, -3) 12 3 4 5 6 7 8 9 10 11 12 What is the equation for the nth term of the arithmetic sequence

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The image features a graph with a series of plotted points that represent an arithmetic sequence. The graph is on a Cartesian plane with labeled axes: the x-axis ranges from 1 to 12, and the y-axis ranges from -3 to 18. The points plotted on the graph are: - (1, -3) - (2, 2) - (3, 7) - (4, 12) - (5, 17) These points reflect a linear pattern, indicating an arithmetic sequence. The common difference between consecutive y-values is 5. The task posed is: "What is the equation for the \(n\)th term of the arithmetic sequence?" To find the equation, observe the sequence of y-values: -3, 2, 7, 12, 17. The first term (when \(n = 1\)) is -3, and the common difference is 5. The formula for the \(n\)th term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1) \cdot d \] Where \(a_1\) is the first term and \(d\) is the common difference. Plugging in the values: \[ a_n = -3 + (n - 1) \cdot 5 \] Simplified, this becomes: \[ a_n = 5n - 8 \] Thus, the equation for the \(n\)th term of the sequence is \(a_n = 5n - 8\).
Transcribed Image Text:The image features a graph with a series of plotted points that represent an arithmetic sequence. The graph is on a Cartesian plane with labeled axes: the x-axis ranges from 1 to 12, and the y-axis ranges from -3 to 18. The points plotted on the graph are: - (1, -3) - (2, 2) - (3, 7) - (4, 12) - (5, 17) These points reflect a linear pattern, indicating an arithmetic sequence. The common difference between consecutive y-values is 5. The task posed is: "What is the equation for the \(n\)th term of the arithmetic sequence?" To find the equation, observe the sequence of y-values: -3, 2, 7, 12, 17. The first term (when \(n = 1\)) is -3, and the common difference is 5. The formula for the \(n\)th term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1) \cdot d \] Where \(a_1\) is the first term and \(d\) is the common difference. Plugging in the values: \[ a_n = -3 + (n - 1) \cdot 5 \] Simplified, this becomes: \[ a_n = 5n - 8 \] Thus, the equation for the \(n\)th term of the sequence is \(a_n = 5n - 8\).
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