Write the first four terms of each sequence whose general term is given. a_n=3n+2

Verified step by step guidance

1. Identify the general term of the sequence, which is given by \(a_n = 3n + 2\).
2. Understand that \(n\) represents the position of the term in the sequence, starting from \(n=1\) for the first term.
3. Calculate the first term by substituting \(n=1\) into the general term: \(a_1 = 3(1) + 2\).
4. Calculate the second term by substituting \(n=2\): \(a_2 = 3(2) + 2\).
5. Continue this process for \(n=3\) and \(n=4\) to find \(a_3 = 3(3) + 2\) and \(a_4 = 3(4) + 2\) respectively.

Key Concepts

Sequences and Terms

A sequence is an ordered list of numbers defined by a specific rule or formula. Each number in the sequence is called a term, and the position of a term is indicated by its index, usually n. Understanding how to identify and write terms from a sequence formula is fundamental.

General Term of a Sequence

The general term (an) of a sequence is a formula that allows you to find any term based on its position n. For example, an = 3n + 2 means to find the nth term, multiply n by 3 and add 2. This formula helps generate terms without listing all previous ones.

Substitution and Evaluation

To find specific terms of a sequence, substitute the term number (n) into the general term formula and simplify. For instance, to find the first four terms, substitute n = 1, 2, 3, and 4 into an = 3n + 2 and calculate each value.