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Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblem 7
Chapter 9, Problem 7

Write the first four terms of each sequence whose general term is given. an=(−1)n(n+3)

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Identify the general term of the sequence given by the formula \(a_n = (-1)^{n}(n+3)\), where \(n\) represents the term number.
To find the first four terms, substitute \(n = 1, 2, 3,\) and \(4\) into the formula one at a time.
Calculate \(a_1\) by substituting \(n=1\): \(a_1 = (-1)^{1}(1+3)\).
Calculate \(a_2\) by substituting \(n=2\): \(a_2 = (-1)^{2}(2+3)\).
Similarly, calculate \(a_3\) and \(a_4\) by substituting \(n=3\) and \(n=4\) into the formula: \(a_3 = (-1)^{3}(3+3)\) and \(a_4 = (-1)^{4}(4+3)\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sequences and General Terms

A sequence is an ordered list of numbers defined by a general term formula a_n, which gives the nth term. Understanding how to use the general term allows you to find specific terms by substituting values of n.
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Evaluating Expressions with Exponents

The term (−1)^n alternates the sign of each term depending on whether n is even or odd. Recognizing this pattern helps determine if a term is positive or negative, which is essential for correctly calculating sequence terms.
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Substitution and Simplification

To find the first four terms, substitute n = 1, 2, 3, and 4 into the general term and simplify each expression. This process involves arithmetic operations and careful handling of signs to accurately compute each term.
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