Arithmetic Sequences and Series

In this lesson, we will learn about arithmetic sequences and series. This is a follow-up to the last two lessons, where we introduced the concepts of both a sequence and a series. We will begin our lesson by defining an arithmetic sequence as a list of numbers with a constant difference between consecutive terms. This constant difference is known as the common difference and is represented with a lowercase d. We will learn how to find the common difference when given some consecutive terms of an arithmetic sequence. Also, we will learn how to find any term in the sequence using the explicit formula a_n = a₁ + (n - 1)d. Once we are comfortable with the idea of an arithmetic sequence, we will then introduce the arithmetic series. An arithmetic series is just the sum of the terms of an arithmetic sequence. We have two main formulas for working with arithmetic series. S_n = (n/2)(a₁ + a_n) and S_n = (n/2)[2a₁ + (n - 1)d]. We will show how to use the formulas to find the sum of an arithmetic series.