Textbook Question
Find the sum of the first 22 terms of the arithmetic sequence: 5, 12, 19, 26, ...
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 9, Problem 21
Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a60 when a1 = 35, d = -3.
Verified step by step guidance1
Identify the given information: the first term \(a_1 = 35\), the common difference \(d = -3\), and the term to find is the 60th term, \(a_{60}\).
Recall the formula for the \(n\)th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\).
Substitute the known values into the formula: \(a_{60} = 35 + (60 - 1) \times (-3)\).
Simplify the expression inside the parentheses: calculate \(60 - 1\) to get 59.
Multiply the common difference by 59 and then add the result to 35 to find \(a_{60}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Arithmetic Sequence
An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference to the previous term. This constant is called the common difference, denoted by d. Understanding this helps identify the pattern and predict any term in the sequence.
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Common Difference (d)
The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence. It can be positive, negative, or zero. In this problem, d = -3 means each term decreases by 3 from the previous term.
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Formula for the nth Term of an Arithmetic Sequence
The nth term (a_n) of an arithmetic sequence is given by a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number. This formula allows calculation of any term, such as a_60, directly without listing all terms.
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