## Introduction to Arithmetic Sequences

### Learning Objectives

By the end of this section, you will be able to:

• Find the common difference for an arithmetic sequence.
• Write terms of an arithmetic sequence.
• Use a recursive formula for an arithmetic sequence.
• Use an explicit formula for an arithmetic sequence.

Companies often make large purchases, such as computers and vehicles, for business use. The book-value of these supplies decreases each year for tax purposes. This decrease in value is called depreciation. One method of calculating depreciation is straight-line depreciation, in which the value of the asset decreases by the same amount each year.

As an example, consider a woman who starts a small contracting business. She purchases a new truck for $25,000. After five years, she estimates that she will be able to sell the truck for$8,000. The loss in value of the truck will therefore be $17,000, which is$3,400 per year for five years. The truck will be worth $21,600 after the first year;$18,200 after two years; $14,800 after three years;$11,400 after four years; and $8,000 at the end of five years. In this section, we will consider specific kinds of sequences that will allow us to calculate depreciation, such as the truck’s value. • Find the common difference for an arithmetic sequence. • Write terms of an arithmetic sequence. • Use a recursive formula for an arithmetic sequence. • Use an explicit formula for an arithmetic sequence. Companies often make large purchases, such as computers and vehicles, for business use. The book-value of these supplies decreases each year for tax purposes. This decrease in value is called depreciation. One method of calculating depreciation is straight-line depreciation, in which the value of the asset decreases by the same amount each year. As an example, consider a woman who starts a small contracting business. She purchases a new truck for$25,000. After five years, she estimates that she will be able to sell the truck for $8,000. The loss in value of the truck will therefore be$17,000, which is $3,400 per year for five years. The truck will be worth$21,600 after the first year; $18,200 after two years;$14,800 after three years; $11,400 after four years; and$8,000 at the end of five years. In this section, we will consider specific kinds of sequences that will allow us to calculate depreciation, such as the truck’s value.