PROGRESSION, in Mathematics, is either arithmetical or geometrical. Continued arithmetic proportion is, where the terms do increase and decrease by equal differences, and is called arithmetic progression:

Thus \left\{ \begin{array}{l} a, a+d, a+2d, a+3d, \&c. \text{ increasing} \\ a, a-d, a-2d, a-3d, \&c. \text{ decreasing} \end{array} \right\} by the difference d.
In numbers \left\{ \begin{array}{l} 2, 4, 6, 8, 10, \&c. \text{ increasing} \\ 10, 8, 6, 4, 2, \&c. \text{ decreasing} \end{array} \right\} by the difference 2.

Geometric Progression, or Continued Geometric Proportion, is when the terms do increase or decrease by equal ratios: thus,

\left\{ \begin{array}{l} a, ar, arr, arrr, \&c. \text{ increasing} \\ a, \frac{a}{r}, \frac{a}{rr}, \frac{a}{rrr}, \&c. \text{ decreasing} \end{array} \right\} from a continual \left\{ \begin{array}{l} \text{multiplication} \\ \text{division} \end{array} \right\} by r.
\left\{ \begin{array}{l} 2, 4, 8, 16, 32, 64, \text{ increasing} \\ 64, 32, 16, 8, 4, 2, \text{ decreasing} \end{array} \right\} from a continual \left\{ \begin{array}{l} \text{multiplication} \\ \text{division} \end{array} \right\} by 2.

See the articles FLUXIONS, GEOMETRY, and SERIES.