![]() ![]() 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 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. Since the question was originally only asking for the value of the third term we know our solution only needs to be the value of the third term which is 9. Step 5: We found the recursive sequence we were looking for: 1,3,9. In this section, we will review sequences that grow in this way. This recursive formula is a geometric sequence. 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. Use an explicit formula for a geometric sequence.Use a recursive formula for a geometric sequence.Example : Find all terms between and of a geometric sequence. Therefore, we can write the general term and the term can be calculated as follows: Answer: The terms between given terms of a geometric sequence are called geometric means21. List the terms of a geometric sequence. The sequence is indeed a geometric progression where and.Find the common ratio for a geometric sequence. ![]()
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