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 in two as so ( is the sum, is the first term, is the number of terms, 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 .
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