Key Concepts & Glossary
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
Licenses & Attributions
CC licensed content, Specific attribution
- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution.