additiveincreasing

Additiveincreasing refers to a property of a sequence or function where each successive term or value is greater than the previous one by a fixed, positive amount. This is a specific type of monotonic sequence or function. In simpler terms, it's like adding the same number over and over again to get the next value.

A common example of an additiveincreasing sequence is an arithmetic progression. For instance, the sequence 2, 5, 8, 11, 14... is additiveincreasing because each term is obtained by adding 3 to the preceding term. The constant positive amount added is called the common difference.

Formally, a sequence (a_n) is additiveincreasing if there exists a constant c > 0 such that a_{n+1} = a_n + c for all n. Similarly, a function f(x) could be described as additiveincreasing over an interval if f(x+h) = f(x) + c for some fixed h > 0 and constant c > 0. However, the term is more commonly applied to sequences. The defining characteristic is the consistent addition of a positive value.