Key Equations
recursive formula for term of a geometric sequence | |
explicit formula for term of a geometric sequence |
Key Concepts
- A geometric sequence is a sequence in which the ratio between any two consecutive terms is a constant.
- The constant ratio between two consecutive terms is called the common ratio.
- The common ratio can be found by dividing any term in the sequence by the previous term.
- The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly.
- A recursive formula for a geometric sequence with common ratio is given by for .
- As with any recursive formula, the initial term of the sequence must be given.
- An explicit formula for a geometric sequence with common ratio is given by .
- In application problems, we sometimes alter the explicit formula slightly to .
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
Candela Citations
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- College Algebra. Authored by: Abramson, Jay et al.. Provided by: OpenStax. Located at: http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@5.2. License: CC BY: Attribution. License Terms: Download for free at http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@5.2
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- Precalculus. Authored by: OpenStax College. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution