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 Answer Button navigates to signup page Comment Button navigates to signup page (15 votes) Upvote. Can anyone explain the basic rules for them Thanks. 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. I find recursive sequences really, really confusing. 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. The yearly salary values described form a geometric sequence because they change by a constant factor each year. 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. It is represented by the formula an a1 + (n-1)d, where a1 is the first term of the sequence, an is the nth term of the sequence, and d is the common difference, which is obtained by subtracting the previous term. Many jobs offer an annual cost-of-living increase to keep salaries consistent with inflation. An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed number to the previous term.
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