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.
To find the sum of an arithmetic sequence, we can write it out as so (S is the sum, a is the first term, n is the number of terms, and d is the common difference):
Now, adding vertically and shifted over one, we get
This equals , so the sum is .
Contents
[hide]Problems
Introductory Problems
Intermediate Problems
Olympiad Problem
See also
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