Arithmetic progression operator

This research paper presents a new way to write arithmetic progressions in a shorter and more structured form. Instead of listing every term or rewriting the same expression repeatedly, the system uses a compact format that stores only the key information: the starting value, the step size, and how many terms are included. It keeps all the usual mathematical properties of arithmetic progressions, works well with algebraic operations, and is easy to apply in both theoretical and applied settings. The goal is to make mathematical writing clearer, faster, and more efficient, especially in areas like number theory, sequences, and computational work