Arithmetic progression

The arithmetic and geometric sequences have well-known historical names and closed-form formulas: they are the two most important families of sequences in elementary arithmetic and recur in finance, physics, population biology, wherever there is “fixed-rate” growth.

Definition — Arithmetic progression (AP)

An arithmetic progression is a sequence $(a_n)$ in which each term is obtained from the previous one by adding a constant $d$, called the common difference: $a_{n+1} = a_n + d,\qquad d\in\mathbb{R}.$ The closed form of the $n$-th term is $a_n = a_1 + (n-1)\,d$ (using indexing from $1$, which is the most common in this context).

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Topics: Sequences
Concepts: Arithmetic progression · Common ratio · General term