![]() 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: I know that a Arithmetic sequence can be modeled by this: Y Y differenceX+ X + start. I know that a Geometric sequence can be modeled by this: Y Y start ( ratio) X X. If you are redistributing all or part of this book in a print format, Shifted Geometric sequence: U0 U 0 start. Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. 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.If you are redistributing all or part of this book in a print format, Multiplying any term of the sequence by the common ratio 6 generates the subsequent term. The sequence below is an example of a geometric sequence because each term increases by a constant factor of 6. Each term of a geometric sequence increases or decreases by a constant factor called the common ratio. Using this formula we can easily calculate the nth term of the Fibonacci sequence as, for. Where is called the Golden Ratio and its value is, 1.618034. ![]() ![]() The yearly salary values described form a geometric sequence because they change by a constant factor each year. The important properties of the Fibonacci Sequence are, We can easily calculate the Fibonacci Numbers using the Binet Formula, Fn (n (1-)n)/5. In this section, we will review sequences that grow in this way. When a salary increases by a constant rate each year, the salary grows by a constant factor. ![]() His salary will be $26,520 after one year $27,050.40 after two years $27,591.41 after three years and so on. His annual salary in any given year can be found by multiplying his salary from the previous year by 102%. He is promised a 2% cost of living increase each year. Suppose, for example, a recent college graduate finds a position as a sales manager earning an annual salary of $26,000. Many jobs offer an annual cost-of-living increase to keep salaries consistent with inflation.
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