Algebra
Basic

Arithmetic Series Sum

Sum of the first n terms of an arithmetic sequence.

Formula

Sn=n2(a1+an)S_n = \frac{n}{2}(a_1 + a_n)

Variables

nNumber of terms
a_1First term
a_nLast term

Example

Sum 1..100 = 100/2 × (1+100) = 5050

Did You Know?

Legend says a young Gauss summed 1 to 100 in seconds by pairing terms — this is the formula he effectively rediscovered.

arithmeticseriessequence