In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=2n/(n+4)

Key Concepts

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 a term is typically denoted by an index, such as 'n'. Understanding how to identify and generate terms from a given formula is essential for working with sequences.

General Term of a Sequence

The general term of a sequence, often denoted as an, is a formula that defines the nth term of the sequence in terms of n. In this case, the general term is given by an = 2n/(n+4). This formula allows us to calculate any term in the sequence by substituting different values of n.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. To find the first four terms of the sequence defined by the general term, we substitute n = 1, 2, 3, and 4 into the formula an = 2n/(n+4). This step is crucial for generating the actual terms of the sequence.