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 · (a0 + an-1) / 2 where:

  • a0 is the first number in the sequence,
  • an-1 is the last number in the sequence, and
  • n is the number of terms.
Applying this to the sequence above, we get:
  • a0 = 2,
  • an-1 = 11, and
  • n = 4.
So,
  • S = 4 · ( 2 + 11 ) / 2
  • S = 4 · 13 / 2
  • S = 52 / 2
  • S = 26.

References

  1. arithmetic progression. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-03-12). http://www.merriam-webster.com/dictionary/arithmetic progression.
  2. 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.

Translations

Image Credits

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.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License