arithmetic series


In mathematics, an arithmetic series is the sum of a finite arithmetic progression. Consider the arithmetic series consisting of the first five terms of arithmetic sequence of natural numbers: 1 + 2 + 3 + 4 + 5. The sum is 15 which is easily calculated using simple addition. For longer series with larger numbers it is more useful to use the following formula to calculate the sum.

For an arithmetic series starting at a number a_1, ending at a number a_n, containing n terms, the sum of the series is:

S = \dfrac{n(a_1 + a_n)}{2}

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