In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3n+2

Verified step by step guidance

1. Identify the general term of the sequence: \(a_n = 3n + 2\).
2. To find the first term, substitute \(n = 1\) into the general term: \(a_1 = 3(1) + 2\).
3. To find the second term, substitute \(n = 2\) into the general term: \(a_2 = 3(2) + 2\).
4. To find the third term, substitute \(n = 3\) into the general term: \(a_3 = 3(3) + 2\).
5. To find the fourth term, substitute \(n = 4\) into the general term: \(a_4 = 3(4) + 2\).

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 each term is typically denoted by an index, such as 'n'. Understanding sequences is fundamental in algebra as they can represent various mathematical concepts, including arithmetic and geometric progressions.

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 the formula an = 3n + 2, where 'n' represents the term's position. This formula is crucial for generating specific terms of the sequence without listing all previous terms.

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