In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n(n+3)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sequences
A sequence is an ordered list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term, and the position of each term is typically denoted by an index, often starting from 1. Understanding how to identify and generate terms from a given rule is essential for working with sequences.
The general term of a sequence is a formula that allows you to calculate any term in the sequence based on its position. In this case, the general term is given by an = (-1)^n(n + 3), where 'n' represents the term's index. This formula combines both arithmetic and alternating signs, which is crucial for determining the specific values of the sequence.
Evaluating expressions involves substituting values into a formula to compute specific results. For the sequence given, you will substitute n = 1, 2, 3, and 4 into the general term to find the first four terms. Mastery of this skill is vital for accurately generating terms from a sequence based on its general term.