8/28/2023 0 Comments Solving sequences anTextbook content produced by OpenStax is licensed under a Creative Commons Attribution License. A) Write down U1 B) Calculate the common difference of the sequence. Use the information below to generate a citation. 1 Hi, I would appreciate if you helped me solving these questions Let Sn be the sum of the first n terms of an arithmetical sequence, whose first three terms are U1 ,U2 and U3. 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, This sequence has a difference of 5 between each number. Example: Write a rule, and calculate the 9th term, for this Arithmetic Sequence: 3, 8, 13, 18, 23, 28, 33, 38. Then you must include on every physical page the following attribution: Rule We can write an Arithmetic Sequence as a rule: xn a + d (n1) (We use 'n1' because d is not used in the 1st term). 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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