OpenStax College, Algebra and Trigonometry. You can also download for free at For questions regarding this license, please contact If you use this textbook as a bibliographic reference, then you should cite it as follows: This work is licensed under a Creative Commons Attribution 4.0 International License. Glossary common ratio the ratio between any two consecutive terms in a geometric sequence geometric sequence a sequence in which the ratio of a term to a previous term is a constant
In application problems, we sometimes alter the explicit formula slightly to. 
An explicit formula for a geometric sequence with common ratio. As with any recursive formula, the initial term of the sequence must be given. A recursive formula for a geometric sequence with common ratio. The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. The common ratio can be found by dividing any term in the sequence by the previous term. The constant ratio between two consecutive terms is called the common ratio. A geometric sequence is a sequence in which the ratio between any two consecutive terms is a constant. Key Equations recursive formula for n t h Multiplying any term of the sequence by the common ratio 6 generates the subsequent term.Īccess these online resources for additional instruction and practice with geometric sequences. 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. Use an explicit formula for a geometric sequence. Use a recursive formula for a geometric sequence. List the terms of a geometric sequence. Find the common ratio for a geometric sequence. 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 Multiplying any term of the sequence by the common ratio 6 generates the subsequent term.
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Find the common ratio for a geometric sequence. Sal finds the 4th term in the sequence whose recursive formula is a(1)-, a(i)2a(i-1).
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