progresjoner

Progresjoner is the plural form of progression, a term used across disciplines to describe a pattern or sequence that develops step by step or in a forward direction. The concept covers mathematical sequences, musical harmony, and broader notions of growth or development over time. In mathematics, progressions are specific types of sequences with defined rules, while in music they describe the order of chords or harmonies.

In mathematics, a progression refers to a sequence with a constant pattern. An arithmetic progression has a constant difference d between successive terms, so the nth term is a_n = a1 + (n − 1)d. The sum of the first n terms is S_n = n/2 (a1 + a_n). A geometric progression has a constant ratio r, so a_n = a1 r^{n−1}. The sum of the first n terms is S_n = a1 (1 − r^n) / (1 − r) for r ≠ 1. Other types include harmonic progressions, where the reciprocals form an arithmetic progression. These progressions are used to model regular increases, decreases, or growth patterns and are widely applied in finance, computer science, and physics.

In music, a progression (chord progression) refers to a sequence of chords that provides harmonic direction and structure. Common progressions, such as I–IV–V–I, establish tonal stability and movement, while more complex progressions create tension and release.

Progresjoner thus describes a broad concept of orderly change, useful for analysis and construction in both abstract and applied contexts.