Arithmetic series
An arithmetic series is a sum of consecutive terms in an arithmetic sequence. For instance,
is an arithmetic series whose value is 50.
Contents
[hide]Formula
To find the sum of an arithmetic sequence, we can write it out in two as so ( is the sum, is the first term, is the last term, and is the common difference): Flipping the right side of the equation we get
Now, adding the above two equations vertically, we get
This equals , so the sum is , where is the number of terms.
Problems
Introductory Problems
Intermediate Problems
Olympiad Problem
See also
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