![]() ![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: For any term in the sequence, weve added. If you are redistributing all or part of this book in a digital format, A recursive definition, since each term is found by adding the common difference to the previous term is ak+1ak+d. Arithmetic Sequence Arithmetic Progression Explicit Formula: an a1 + (n 1)d Example 1: 3, 7, 11, 15, 19 has a1 3, d 4, and n 5. 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. Explicit formula is used to find the nth term of the sequence using one or more preceding terms of the sequence. ![]() To write the recursive rule there are three steps to follow. A recursive formula allows us to find any term of an arithmetic sequence using a function of the preceding term. Recursive formula is used to find the next term of the sequence using one or more preceding terms of the sequence. a1, an a (n-1) +d Consider an example arithmetic sequence. For this sequence, the common difference is –3,400. The recursive rule of an arithmetic sequence gives the first term of the sequence and a recursive equation. 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. applied math, logic functions, arithmetic, calculus, etc. 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 proof problem consists of showing that the goal formula, under the assump- In. 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. Write a recursive formula for the arithmetic sequence tn given below. 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. ![]()
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