Common Difference
Pronunciation: /ˈkɒm ən ˈdɪf ər əns/ Explain
The common difference in an
arithmetic sequence
is the constant difference between any term and the term after it.^{[1]}
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.
- What is the common difference of { 4, 7, 10, 13 }?
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7 - 4 = 3, 10 - 7 = 3, 13 - 10 = 3 The common difference is 3.
- What is the common difference of { -1, 1, 3, 5 }?
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1 - (-1) = 2, 3 - 1 = 2, 5 - 3 = 2 The common difference is 2.
- What is the common difference of { 4, 6, 9, 13 }?
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6 - 4 = 2, 9 - 6 = 3 There is no common difference.
- What is the next number in the sequence { 1, 5, 9, ? }?
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5 - 1 = 4, 9 - 5 = 4 The next number in the sequence is 9 + 4 = 13.
- What is the next number in the sequence { 2, 4, 6, ? }?
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4 - 2 = 2, 6 - 4 = 2 The next number in the sequence is 6 + 2 = 8.
References
- common difference. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018. http://www.merriam-webster.com/dictionary/common difference.
- Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 260-262. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/6/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n277/mode/1up/search/progression. Buy the book
- Rivenburg, Romeyn Henry. A Review of Algebra. pg 47. www.archive.org. American Book Company. 1914. Last Accessed 8/6/2018. http://www.archive.org/stream/reviewofalgebra00riverich#page/47/mode/1up/search/progression. Buy the book
Cite this article as:
McAdams, David E. Common Difference. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/commondifference.html.
Image Credits
Revision History
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.)