12n

12n is an algebraic expression that denotes the product of the integer 12 and a variable n. When n is restricted to integers, 12n represents a multiple of 12 and describes a simple linear map from n to the integers. The set of all numbers of the form 12n with n in Z is the set of all multiples of 12, i.e., -24, -12, 0, 12, 24, 36, and so on. If n is a natural number, 12n forms the sequence of positive multiples of 12 starting at 12.

In algebra, 12n is a homogeneous linear form and is often used to test divisibility properties: any number of the form 12n is divisible by 12, and 12n is congruent to 0 modulo 12. In contexts where n represents a parameter, 12n describes a family of values that scale by 12 per unit increase in n.

Examples: n = 1 yields 12; n = 5 yields 60; n = 0 yields 0; n = -3 yields -36.

The expression is also encountered in arithmetic progressions, where the terms have a common difference of 12. In programming, 12n may appear in loops or formulas computing sizes, indices, or steps that advance in increments of 12.

Related concepts include multiples and divisibility by 12, arithmetic progressions with difference 12, and linear functions of the form kn where k is a fixed integer.