pentagonal number

A pentagonal number is a figurate number that represents a pentagon. It is a number that can be arranged in the shape of a regular pentagon, typically formed by dots or units. The nth pentagonal number is given by the formula ( P_n = frac{3n^2 – n}{2} ), where ( n ) is a positive integer. Pentagonal numbers have applications in number theory and combinatorics, and they often appear in mathematical problems involving polygonal shapes and sequences.