Definition:Arithmetic Series

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Definition

An arithmetic series is a series whose underlying sequence is an arithmetic progression:


\(\displaystyle S_n\) \(=\) \(\displaystyle \sum_{k \mathop = 0}^{n - 1} a + k d\)
\(\displaystyle \) \(=\) \(\displaystyle a + \left({a + d}\right) + \left({a + 2 d}\right) + \cdots + \left({a + \left({n - 1}\right) d}\right)\)


Linguistic Note

In the context of an arithmetic progression or arithmetic-geometric progression, the word arithmetic is pronounced with the stress on the first and third syllables: a-rith-me-tic, rather than on the second syllable: a-rith-me-tic.

This is because the word is being used in its adjectival form.


Sources