Write the first four terms of each sequence whose general term is given. a_n = 7n - 4

Verified step by step guidance

1. Identify the general term of the sequence, which is given as \(a_n = 7n - 4\), where \(n\) represents the term number.
2. To find the first term (\(a_1\)), substitute \(n = 1\) into the general term: \(a_1 = 7(1) - 4\).
3. To find the second term (\(a_2\)), substitute \(n = 2\) into the general term: \(a_2 = 7(2) - 4\).
4. To find the third term (\(a_3\)), substitute \(n = 3\) into the general term: \(a_3 = 7(3) - 4\).
5. To find the fourth term (\(a_4\)), substitute \(n = 4\) into the general term: \(a_4 = 7(4) - 4\).

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 n. Understanding how to identify and write terms from a general formula is fundamental.

General Term Formula

The general term formula, a_n, expresses the nth term of a sequence as a function of n. For example, a_n = 7n - 4 means to find the nth term, multiply n by 7 and subtract 4. This formula allows calculation of any term without listing all previous terms.

Evaluating Terms of a Sequence

To find specific terms, substitute values of n (starting from 1) into the general term formula. For the first four terms, calculate a_1, a_2, a_3, and a_4 by plugging in n = 1, 2, 3, and 4 respectively. This process helps generate the sequence explicitly.