Arithmetic Sequence Calculator
Find any term and the cumulative sum of an arithmetic sequence. Enter the first term, common difference, and the desired term number to get instant results along with a sequence preview.
An arithmetic sequence (or arithmetic progression) is a sequence of numbers where the difference between consecutive terms is constant. This constant is called the common difference (d). For example, the sequence 2, 5, 8, 11, 14 has a common difference of 3.
The nth term of an arithmetic sequence is given by aₙ = a₁ + (n-1)d, where a₁ is the first term and d is the common difference. The sum of the first n terms is Sₙ = n/2 × (2a₁ + (n-1)d), which can also be written as Sₙ = n/2 × (a₁ + aₙ), the average of the first and last term multiplied by the number of terms.
Arithmetic sequences appear throughout mathematics and everyday life: equally spaced payments, linear depreciation, stacking patterns, and evenly distributed points. The famous story of young Gauss summing the integers from 1 to 100 (getting 5050) uses the arithmetic series sum formula with a₁ = 1, d = 1, and n = 100.