Common Ratio
Pronunciation: /ˈkɒm ən ˈreɪ ʃoʊ/ ?
- 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.
- 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
- geometric ratio. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-04). http://www.merriam-webster.com/dictionary/geometric ratio.
- 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). http://www.archive.org/stream/academicalgebraf00bowsrich#page/324/mode/1up/search/geometric.
- Nicholson, J. W.. School Algebra, pg 271. American Book Company, 1909. (Accessed: 2010-02-06). http://www.archive.org/stream/schoolalgebra00nichgoog#page/n273/mode/1up.
Printed Resources
Cite this article as:
Common Ratio. 2010-01-04. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/commonratio.html.
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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.)