In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a6 when a₁ = 13, d = 4.

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference (d). The general form of an arithmetic sequence can be expressed as a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and n is the term number.

First Term (a₁)

The first term of an arithmetic sequence, denoted as a₁, is the initial value from which the sequence begins. In this case, a₁ = 13 indicates that the first term of the sequence is 13. This value is crucial for calculating subsequent terms in the sequence using the common difference.

Common Difference (d)

The common difference (d) in an arithmetic sequence is the fixed amount added to each term to obtain the next term. For this problem, d = 4 means that each term in the sequence increases by 4 from the previous term. Understanding the common difference is essential for determining any term in the sequence, including a₆.