Arithmetic Nth Term Calculator

About this calculator

An arithmetic sequence increases (or decreases) by the same fixed amount, the common difference (d), from one term to the next. Any term can be found directly without listing every value before it, using aₙ = a₁ + (n−1)d, where a₁ is the first term and n is the position you want.

The same sequence has a matching shortcut for adding up its first n terms: Sₙ = n/2 × (2a₁ + (n−1)d), avoiding tedious term-by-term addition. This is foundational algebra taught in middle and high school, and it comes up anywhere a quantity changes by a constant step each period — seating rows in a theater, stacked objects, or simple interest-style linear growth problems.