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

#### Understanding check

What is the next element of the geometric sequence { 2, 6, 18, ? }? Click here to see answer.

### 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

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.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)