Progression

Progression, in Arithmetic, is the succession, according to some fixed law, of one number after another. A series of numbers so succeeding one another is said to be 'in progression.' Progression may be of various kinds, but the three forms of most frequent occurrence are Arithmetical Progression (q.v.), Geometrical Progression (q.v.), and Harmonical Progression. If the terms of an arithmetical progression be inverted they form a series in harmonical progression; thus, 1, 2, 3, 4, 5, 6, &c. is an arithmetical progression; and 1, $\backslash frac\{1\}\{2\}$, $\backslash frac\{1\}\{3\}$, $\backslash frac\{1\}\{4\}$, $\backslash frac\{1\}\{5\}$, $\backslash frac\{1\}\{6\}$, &c. is a harmonical progression. This series is principally important in connection with the theory of music, in determining the length of the strings of instruments. See HARMONICS.