Arithmetic Series Sum Calculator

About this calculator

An arithmetic series is the sum of a sequence where each term increases by the same fixed amount, called the common difference (d). Its sum is found without adding every term individually, using the formula S = n/2 × (2a + (n−1)d), where a is the first term and n is the number of terms — a shortcut famously attributed to a young Gauss summing 1 through 100.

This calculator takes the first term, common difference, and number of terms, and returns the total sum along with the nth (last) term and the average term (which for any arithmetic series equals the sum divided by n, and also the midpoint between the first and last terms). It's a standard tool for algebra and precalculus students checking series problems or exploring how the formula behaves for different sequences.