Common Ratio

Pronunciation: /ˈkɒm ən ˈreɪ ʃoʊ/ ?
  1. The common ratio in a geometric sequence is the constant ratio between any term and the term after it.[1] 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.

check mark 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.

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

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


  1. geometric ratio. Encyclopedia Britannica. (Accessed: 2010-01-04). ratio.
  2. Bowser, Edward A.. Academic algebra : for the use of common and high schools and academies, pp 324-326. D. C. Heath & Co., 1895. (Accessed: 2010-02-06).
  3. Nicholson, J. W.. School Algebra, pg 271. American Book Company, 1909. (Accessed: 2010-02-06).

Printed Resources

Cite this article as:

Common Ratio. 2010-01-04. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2010-02-06: Added "References" (McAdams, David.)
2009-10-26: Added definition for geometric ratio. (McAdams, David.)
2008-08-13: Added definition 2; added More Information (McAdams, David.)
2008-07-07: Added Finding the Common Ratio and Understanding Check (McAdams, David.)
2007-12-12: Initial version (McAdams, David.)

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