One definition where we write it like this, or weĬould write a sub n, from n equals 1 to infinity. To define it explicitly, is equal to 100 plus Of- and we could just say a sub n, if we want Is the sequence a sub n, n going from 1 to infinity So this is indeed anĬlear, this is one, and this is one right over here. Is this one arithmetic? Well, we're going from 100. The arithmetic sequence that we have here. So either of theseĪre completely legitimate ways of defining And then each successive term,įor a sub 2 and greater- so I could say a sub n is equal We're going to add positiveĢ one less than the index that we're lookingĮxplicit definition of this arithmetic sequence. So for the secondįrom our base term, we added 2 three times. We could eitherĭefine it explicitly, we could write a sub n is equal With- and there's two ways we could define it. So this is clearly anĪrithmetic sequence. Then to go from negativeġ to 1, you had to add 2. These are arithmetic sequences? Well let's look at thisįirst one right over here. Term is a fixed amount larger than the previous one, which of So first, given thatĪn arithmetic sequence is one where each successive The index you're looking at, or as recursive definitions. And then just so thatĮither as explicit functions of the term you're looking for, Out which of these sequences are arithmetic sequences. Term is a fixed number larger than the term before it. Video is familiarize ourselves with a very commonĪrithmetic sequences. 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: 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.
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