Write the Terms of an Arithmetic Sequence

We will explore two kinds of sequneces in this unit. The first is the arithmetic sequence. In this section, you will learn the characteristics of arithmetic sequences and use a formula to find the terms.

Arithmetic Sequences

Learning Objectives

In this section, you will:

  • 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.

Source: Rice University, https://openstax.org/books/college-algebra/pages/9-2-arithmetic-sequences
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