Arithmetic Series
Pronunciation: /æ.rɪθˈmɛ.tɪk ˈsɪər.iz/ Explain
An arithmetic series is the sum of an
arithmetic sequence.^{[2]}
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
- McAdams, David E.. All Math Words Dictionary, arithmetic series. 2nd Classroom edition 20150108-4799968. pg 20-21. Life is a Story Problem LLC. January 8, 2015. Buy the book
- arithmetic progression. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/12/2018. https://www.merriam-webster.com/dictionary/arithmetic%20progression. Buy the book
- Kelso, Oscar Lynn, M.A.. Arithmetic for High Schools, Academies, and Normal Schools. pg 265. www.archive.org. The Macmillan Company. 1903. Last Accessed 6/12/2018. http://www.archive.org/stream/arithmeticforhi00kelsgoog#page/n281/mode/1up/search/series. Buy the book
Cite this article as:
McAdams, David E. Arithmetic Series. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/arithmeticseries.html.
Revision History
4/12/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
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.)