Which sequences are arithmetic4/10/2023 ![]() ![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. In each of these sequences, the difference between consecutive terms is constant, and so the sequence is arithmetic. The difference between consecutive terms, is d, the common difference, for n greater than or equal to two. Use the information below to generate a citation. An arithmetic sequence is a sequence where the difference between consecutive terms is always the same. The constant is called the common difference. Then you must include on every digital page view the following attribution: Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant. 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. We can find Sn by simply summing all terms together: Sn 1 + 3 + 5 + 7. Because we always add 2 to get to the next term, our common difference d is 2. The first term, a1, is 1, and the last term, an, is 7. In this case, the constant difference is 3. Solution: In this example, we have four terms and thus n 4. ![]() 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. In this section, we will consider specific kinds of sequences that will allow us to calculate depreciation, such as the truck’s value. 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. An arithmetic sequence is an ordered list usually of numbers such that there is a common difference between terms. 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. The book-value of these supplies decreases each year for tax purposes. This difference can either be positive or negative, and dependent on the sign will result in terms of the arithmetic sequence tending towards positive or negative infinity.
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