Common Ratio

Pronunciation: /ˈkɒm.ən ˈreɪ.ʃoʊ/ Explain

1. The common ratio in a geometric sequence is the constant ratio between any term and the term after it.^[2][3] A common ratio is also called a geometric ratio.

   For example, the geometric sequence { 1, 3, 9, 27 } has a common ratio of 3. You can see that 1 · 3 = 3, and 3 · 3 = 9. Check the rest of the terms. Each term is 3 times the term before it.

2. A common ratio of two variables is a number that, when multiplied by one of the variables, gives the other. The general equation for a common ratio is y = ax where y and x are the variables and a is the common ratio. This is most often called the constant of variation.

Finding the Common Ratio of a Geometric Sequence

What is the common ratio of { 2, 4, 8, 16 }?

2·2 = 4, 4·2 = 8, 8·2 = 16 The common ratio is 2.

Understanding check

Find the common ratio of each geometric sequence. Then click on Click here to see answer to see the answer.

What is the common ratio of { 3, 9, 27 }? Click here to see answer. 3·3 = 9, 9·3 = 27. The common ratio is 3.

What is the common ratio of { 1, 5, 25 }? Click here to see answer. 1·5 = 5, 5·5 = 25. The common ratio is 5.

What is the next element of the geometric sequence { 2, 6, 18, ? }? Click here to see answer. 2·3 = 6, 6·3 = 18. The common ratio is 3. The next entry is 18·3 = 54.

References

1. McAdams, David E.. All Math Words Dictionary, common ratio. 2nd Classroom edition 20150108-4799968. pg 37. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Bowser, Edward A.. Academic algebra : for the use of common and high schools and academies. pp 324-326. www.archive.org. D. C. Heath & Co.. 1895. Last Accessed 6/25/2018. http://www.archive.org/stream/academicalgebraf00bowsrich#page/324/mode/1up/search/geometric. Buy the book
3. Nicholson, J. W.. School Algebra. pg 271. www.archive.org. American Book Company. 1909. Last Accessed 6/25/2018. http://www.archive.org/stream/schoolalgebra00nichgoog#page/n273/mode/1up. Buy the book

Cite this article as:

McAdams, David E. Common Ratio. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/commonratio.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
2/6/2010: Added "References". (McAdams, David E.)
10/26/2009: Added definition for geometric ratio. (McAdams, David E.)
8/13/2008: Added definition 2; added More Information. (McAdams, David E.)
7/7/2008: Added Finding the Common Ratio and Understanding Check. (McAdams, David E.)
12/12/2007: Initial version. (McAdams, David E.)