arithmetic progressions

An arithmetic progression is a sequence of numbers where each term increases or decreases by a fixed amount, called the common difference. For example, 3, 7, 11, 15, ... has a common difference of 4. This pattern can continue indefinitely in either direction. Arithmetic progressions are useful for modeling situations involving consistent changes, such as saving a fixed amount each month or traveling at a steady speed. The key characteristics are the initial term and the common difference, which together determine the entire sequence.