Pentagonal numbers are a type of figurate number that represent a pentagon. They can be calculated using the formula P_n = \fracn(3n - 1)2 , where n is a positive integer. The first few pentagonal numbers are 1, 5, 12, 22, and 35. These numbers can be visualized by arranging dots in the shape of a pentagon. These numbers are part of a broader category known as polygonal numbers, which includes triangular and square numbers. Pentagonal numbers have interesting properties and relationships with other figurate numbers, making them a subject of study in number theory.