![]() 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 As with any recursive formula, the initial term must be given. Then each term is nine times the previous term. For example, suppose the common ratio is 9. Each term is the product of the common ratio and the previous term. Suppose you want to find the 10th term of the sequence. A recursive formula allows us to find any term of a geometric sequence by using the previous term. 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. Now that we have our explicit formula for the geometric sequence, we can find any term within that sequence. 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. Step 4: We can check our answer by adding the difference, d to each term in the sequence to check whether the next term in the sequence is correct or not. Each term of a geometric sequence increases or decreases by a constant factor called the common ratio. Step 3: Repeat the above step to find more missing numbers in the sequence if there. ![]() 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. Use an explicit formula for a geometric sequence. ![]() ![]()
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