To find the explicit and recursive formulas for this sequence, we need to determine the first term. Explanation: The geometric sequence given is 5, 20, 80, 320. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Final answer: The explicit formula for the given geometric sequence is a 5 × 4¹, and the recursive formula is a a × 4, with an initial condition of a 5. 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 need to review these topics, click here. In this lesson, it is assumed that you know what an arithmetic sequence is and can find a common difference. If you are redistributing all or part of this book in a print format, This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence. ![]() 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. ![]() 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. Many jobs offer an annual cost-of-living increase to keep salaries consistent with inflation.
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