Arithmetic Series Sum Calculator

About this calculator

The sum of an arithmetic series — a sequence where each term increases by a constant common difference d — is given by Sn = n/2 × (2a + (n − 1) × d), where a is the first term and n is the number of terms; this is equivalent to the more famous form Sn = n × (first term + last term) divided by 2, attributed to the young Carl Friedrich Gauss, who reportedly summed 1 through 100 instantly by pairing terms from opposite ends.

Arithmetic series appear whenever a quantity changes by a fixed amount each step — calculating total savings when depositing a fixed amount plus regular fixed increases, seating arrangements that add a constant number of seats per row, simple-interest style linear growth, and stacked-object counting problems (like bricks in a triangular pile) are all arithmetic series in disguise, making the formula a staple of algebra and discrete math courses.

This calculator takes the first term, common difference, and number of terms and instantly returns both the sum of the series and its last term.