Arithmetical progression definitions

Webster's 1913 Dictionary

Progression Pro*gres"sion, n. [L. progressio: cf. F. progression.] 1. The act of moving forward; a proceeding in a course; motion onward. 2. Course; passage; lapse or process of time. I hope, in a short progression, you will be wholly immerged in the delices and joys of religion. --Evelyn. 3. (Math.) Regular or proportional advance in increase or decrease of numbers; continued proportion, arithmetical, geometrical, or harmonic. 4. (Mus.) A regular succession of tones or chords; the movement of the parts in harmony; the order of the modulations in a piece from key to key. Arithmetical progression, a progression in which the terms increase or decrease by equal differences, as the numbers [lbrace2]2, 4, 6, 8, 1010, 8, 6, 4, 2[rbrace2] by the difference 2. Geometrical progression, a progression in which the terms increase or decrease by equal ratios, as the numbers [lbrace2]2, 4, 8, 16, 32, 6464, 32, 16, 8, 4, 2[rbrace2] by a continual multiplication or division by 2. Harmonic progression, a progression in which the terms are the reciprocals of quantities in arithmetical progression, as 1/2, 1/4, 1/6, 1/8, 1/10.

Webster's 1913 Dictionary

Arithmetical Ar`ith*met"ic*al, a. Of or pertaining to arithmetic; according to the rules or method of arithmetic. Arithmetical complement of a logarithm. See Logarithm. Arithmetical mean. See Mean. Arithmetical progression. See Progression. Arithmetical proportion. See Proportion.