freeCodeCamp/guide/english/mathematics/arithmetic-sequence/index.md

title
Arithmetic Sequence

Arithmetic Sequence

An arithmetic sequence, or arithmetic progression, is a sequence of numbers where the difference between each consecutive number is the same.

If n is the placement of some term in the sequence (e.g. 1, 2, 3...), d is the difference between each consecutive term, k is the first the placement of the first known term of the sequence (e.g. if you know the first term, then k = 1), a_k is the value of the k^th term in the sequence (i.e. the value at term number k), and a_n is the value of the n^th term in the sequence (i.e. the value at term number n), then the equation for an arithmetic sequence is this¹:

a_n = a_k + d(n - k)

Sources

1. "Arithmetic Progressions." Brilliant.org. October 1, 2018.