Textbook Question
Write the first four terms of each sequence whose general term is given.
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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 1
Write the first four terms of each sequence whose general term is given. an=3n+2
Verified step by step guidance1
Identify the general term of the sequence, which is given by \(a_n = 3n + 2\).
Understand that \(n\) represents the position of the term in the sequence, starting from \(n=1\) for the first term.
Calculate the first term by substituting \(n=1\) into the general term: \(a_1 = 3(1) + 2\).
Calculate the second term by substituting \(n=2\): \(a_2 = 3(2) + 2\).
Continue this process for \(n=3\) and \(n=4\) to find \(a_3 = 3(3) + 2\) and \(a_4 = 3(4) + 2\) respectively.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sequences and Terms
A sequence is an ordered list of numbers defined by a specific rule or formula. Each number in the sequence is called a term, and the position of a term is indicated by its index, usually n. Understanding how to identify and write terms from a sequence formula is fundamental.
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Introduction to Sequences
General Term of a Sequence
The general term (an) of a sequence is a formula that allows you to find any term based on its position n. For example, an = 3n + 2 means to find the nth term, multiply n by 3 and add 2. This formula helps generate terms without listing all previous ones.
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Substitution and Evaluation
To find specific terms of a sequence, substitute the term number (n) into the general term formula and simplify. For instance, to find the first four terms, substitute n = 1, 2, 3, and 4 into an = 3n + 2 and calculate each value.
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