Arithmetic Progressions — Definition

Definition

An arithmetic progression is an ordered sequence in which the difference between consecutive terms stays constant. That fixed difference can be positive, negative or zero. The sequence 8, 13, 18, 23 is an arithmetic progression with common difference 5; 8, 16, 32 is not, because its differences change.

The idea models equal additions over equal steps, such as a fixed increase in seats from one row to the next. It should not be confused with equal percentage growth, which generally produces changing absolute increments.

Knowing the first term and common difference determines every later term.