Arithmetic Series Formulas

Below are some arithmetic series formulas for sum of arithmetic series. You can also find arithmetic series formulas on Math Worksheets. Arithmetic series formulas are very useful to calculate quick math answers.

Arithmetic series formulas: for any a and d

The sum of the arithmetic series below is given by the arithmetic series formula:

a + (a+d) + (a+2d) + ..... + {a+(n-1)d}

= ½n{2a + (n-1)d}

= ½n(a+l)

Where l = a + (n-1)d is the last term. In another word:

and the arithmetic series formula above is:

Arithmetic series formulas: for special cases

The first of the special cases of the arithmetic series is the sum of consecutive numbers as shown below. The arithmetic series formula for this is:

Another useful arithmetic series formula is this: