Arithmetic Series
Pronunciation: /əˈrɪθmə tɪk ˈsɪər iz/ ?
An arithmetic series is the sum of an
arithmetic sequence.^{[1]}
For example, the arithmetic series for the sequence { 2, 5, 8, 11 }
is 2 + 5 + 8 + 11 = 26.
The general formula for an arithmetic series is
S = n · (a_{0} + a_{n-1}) / 2 where:
- a_{0} is the first number in the sequence,
- a_{n-1} is the last number in the sequence, and
- n is the number of terms.
Applying this to the sequence above, we get:
- a_{0} = 2,
- a_{n-1} = 11, and
- n = 4.
So,
- S = 4 · ( 2 + 11 ) / 2
- S = 4 · 13 / 2
- S = 52 / 2
- S = 26.
References
- arithmetic progression. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-03-12). http://www.merriam-webster.com/dictionary/arithmetic progression.
- Kelso, Oscar Lynn, M.A.. Arithmetic for High Schools, Academies, and Normal Schools, pg 265. The Macmillan Company, 1903. (Accessed: 2010-01-06). http://www.archive.org/stream/arithmeticforhi00kelsgoog#page/n281/mode/1up/search/series.
Cite this article as:
Arithmetic Series. 2010-01-06. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/arithmeticseries.html.
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Revision History
2010-01-06: Added "References" (
McAdams, David.)
2008-06-07: Corrected spelling (
McAdams, David.)
2008-02-03: Added general formula for an arithmetic series (
McAdams, David.)
2007-08-08: Initial version (
McAdams, David.)