In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 7n - 4

Key Concepts

Sequences

A sequence is an ordered list of numbers that follow a specific rule or pattern. Each number in the sequence is called a term, and the position of each term is typically denoted by an index, such as 'n'. Understanding sequences is fundamental in algebra as they form the basis for more complex mathematical concepts, including series and functions.

General Term

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 a_n = 7n - 4, where 'n' represents the term's position. This formula is crucial for generating specific terms of the sequence and understanding its behavior as 'n' changes.

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 a_n = 7n - 4, you substitute n with the values 1, 2, 3, and 4. This technique is essential for evaluating expressions and understanding how changes in input affect the output.