Common Difference

Pronunciation: /ˈkɒm.ən ˈdɪ.frəns/ Explain

The common difference in an arithmetic sequence is the constant difference between any term and the term after it.^[2][3][4]

For example, the arithmetic sequence { 1, 3, 5, 7, 9 } has a common difference of 2. You can see that 3 - 1 = 2, and 5 - 3 = 2. Check the rest of the terms. Each term is 2 more than the term before it.

Understanding check

Write down the answer to the question, then click on Click here for answer to see the answer.

1. What is the common difference of { 4, 7, 10, 13 }? Click here for answer 7 - 4 = 3, 10 - 7 = 3, 13 - 10 = 3 The common difference is 3.
2. What is the common difference of { -1, 1, 3, 5 }? Click here for answer 1 - (-1) = 2, 3 - 1 = 2, 5 - 3 = 2 The common difference is 2.
3. What is the common difference of { 4, 6, 9, 13 }? Click here for answer 6 - 4 = 2, 9 - 6 = 3 There is no common difference.
4. What is the next number in the sequence { 1, 5, 9, ? }? Click here for answer 5 - 1 = 4, 9 - 5 = 4 The next number in the sequence is 9 + 4 = 13.
5. What is the next number in the sequence { 2, 4, 6, ? }? Click here for answer 4 - 2 = 2, 6 - 4 = 2 The next number in the sequence is 6 + 2 = 8.

References

1. McAdams, David E.. All Math Words Dictionary, common difference. 2nd Classroom edition 20150108-4799968. pg 37. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. common difference. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/25/2018. http://www.merriam-webster.com/dictionary/common difference. Buy the book
3. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 260-262. www.archive.org. International Textbook Company. January 1963. Last Accessed 6/25/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n277/mode/1up/search/progression. Buy the book
4. Rivenburg, Romeyn Henry. A Review of Algebra. pg 47. www.archive.org. American Book Company. 1914. Last Accessed 6/25/2018. http://www.archive.org/stream/reviewofalgebra00riverich#page/47/mode/1up/search/progression. Buy the book

Cite this article as:

McAdams, David E. Common Difference. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/commondifference.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.)
1/4/2010: Added "References". (McAdams, David E.)
7/7/2008: Added understanding check. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)