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

Verified step by step guidance

1. Identify the general term of the sequence, which is given as \(a_n = 3^{n}\).
2. Recall that the sequence terms are found by substituting values of \(n\) starting from 1 into the general term.
3. Calculate the first term by substituting \(n=1\) into the formula: \(a_1 = 3^{1}\).
4. Calculate the second term by substituting \(n=2\): \(a_2 = 3^{2}\).
5. Continue this process for \(n=3\) and \(n=4\) to find \(a_3 = 3^{3}\) and \(a_4 = 3^{4}\) 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 n. Understanding how to identify and write terms from a general formula is fundamental.

General Term of a Sequence

The general term, often denoted as a_n, is a formula that defines the nth term of a sequence. It allows you to find any term in the sequence by substituting the value of n. For example, a_n = 3^n means each term is 3 raised to the power of n.

Exponents and Powers

Exponents indicate repeated multiplication of a base number. In the expression 3^n, 3 is the base and n is the exponent, meaning multiply 3 by itself n times. Understanding how to calculate powers is essential to evaluate terms in sequences like a_n = 3^n.