![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. What is an arithmetic sequence For many of the examples above, the pattern involves adding or subtracting a number to each term to get the next term. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the You can choose any term of the sequence, and add 3 to find the subsequent term. In this case, the constant difference is 3. The sequence below is another example of an arithmetic sequence. For this sequence, the common difference is –3,400. Each term increases or decreases by the same constant value called the common difference of the sequence. The values of the truck in the example are said to form an arithmetic sequence because they change by a constant amount each year. The constant difference is called common difference of that arithmetic progression. In this section, we will consider specific kinds of sequences that will allow us to calculate depreciation, such as the truck’s value. An arithmetic progression or arithmetic sequence ( AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. 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. The loss in value of the truck will therefore be $17,000, which is $3,400 per year for five years. ![]() After five years, she estimates that she will be able to sell the truck for $8,000. One method of calculating depreciation is straight-line depreciation, in which the value of the asset decreases by the same amount each year.Īs an example, consider a woman who starts a small contracting business. This decrease in value is called depreciation. Definition: An arithmetic sequence is one in which the difference (aka common. By using the general term with 4 and 3, the t h term of this sequence is given by. In an arithmetic sequence, the difference of consecutive terms is constant. They are defined by recurrence relations. It has a first term 4 and a common difference of 3. ![]() For instance, the sequence 4, 1, 2, 5, 8, is an example of an arithmetic sequence. The book-value of these supplies decreases each year for tax purposes. An arithmetic series is the sum of a given number of terms of an arithmetic sequence.
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