Write the first four terms of each sequence whose general term is given. a_n=2n/(n+4)

Verified step by step guidance

1. Identify the general term of the sequence given by \(a_n = \frac{2n}{n+4}\), where \(n\) represents the term number.
2. Calculate the first term by substituting \(n=1\) into the formula: \(a_1 = \frac{2(1)}{1+4}\).
3. Calculate the second term by substituting \(n=2\) into the formula: \(a_2 = \frac{2(2)}{2+4}\).
4. Calculate the third term by substituting \(n=3\) into the formula: \(a_3 = \frac{2(3)}{3+4}\).
5. Calculate the fourth term by substituting \(n=4\) into the formula: \(a_4 = \frac{2(4)}{4+4}\).

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, an, expresses the nth term of a sequence as a function of n. By substituting different values of n (usually positive integers), you can find specific terms in the sequence. This formula allows you to generate any term without listing all previous terms.

Substitution and Simplification

To find terms of a sequence from the general term, substitute values of n into the formula and simplify the expression. This involves basic algebraic manipulation such as fraction simplification and arithmetic operations to obtain the numerical value of each term.