![]() 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. 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. 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. Use an explicit formula for an arithmetic sequence.Ĭompanies often make large purchases, such as computers and vehicles, for business use.Use a recursive formula for an arithmetic sequence.Find the common difference for an arithmetic sequence.d = the common difference (the difference between every term and its previous term.a = the first term of the arithmetic sequence.\(a_n\) = n th term of the arithmetic sequence.The n th term of the arithmetic sequence represents the explicit formula of the arithmetic sequence. The formula for the common difference is d = a 2 - a 1 = a 3 - a 2 = a n - a n - 1. Here the first term is referred as 'a' and we have a = a 1 and the common difference is denoted as 'd'. The arithmetic sequence is a 1, a 2, a 3. ![]() It helps to easily find any term of the arithmetic sequence. The arithmetic sequence explicit formula is derived from the terms of the arithmetic sequence. ![]() The arithmetic sequence explicit formula is a n = a + (n - 1)d.ĭerivation of Arithmetic Sequence Explicit Formula This formula gives the n th term formula of an arithmetic sequence. ![]() , a n. using its first term (a) and the common difference (d). The arithmetic sequence explicit formula is used to find any term (n th term) of the arithmetic sequence, a 1, a 2, a 3. What Is Arithmetic Sequence Explicit Formula? Let us learn the arithmetic sequence explicit formula, and its derivation with the help of examples, FAQs. Here the arithmetic sequence explicit formula (a n = 3n - 1) is useful to find any terms of the series and can be calculated without knowing the previous term. The arithmetic sequence explicit formula for this series is a n = a + (n - 1)d, or a n = 2 + (n - 1)3 or a n = 3n - 1. the first term is a = 2, and the common difference is d = 5 - 2 = 3. An arithmetic sequence is a sequence of numbers in which the differences between any two consecutive numbers are the same. Arithmetic sequence explicit formula is useful to find any terms of the given arithmetic sequence. ![]()
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