Arithmetic Series

Pronunciation: /əˈrɪθmə tɪk ˈsɪər iz/ Explain

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. Merriam-Webster. Last Accessed 8/6/2018. https://www.merriam-webster.com/dictionary/arithmetic%20progression.
  2. Kelso, Oscar Lynn, M.A.. Arithmetic for High Schools, Academies, and Normal Schools. pg 265. www.archive.org. The Macmillan Company. 1903. Last Accessed 8/6/2018. http://www.archive.org/stream/arithmeticforhi00kelsgoog#page/n281/mode/1up/search/series. Buy the book

Cite this article as:

McAdams, David E. Arithmetic Series. 6/15/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/arithmeticseries.html.

Revision History

6/15/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
1/6/2010: Added "References". (McAdams, David E.)
6/7/2008: Corrected spelling. (McAdams, David E.)
2/3/2008: Added general formula for an arithmetic series. (McAdams, David E.)
8/8/2007: Initial version. (McAdams, David E.)

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