Number Theory
Intermediate

Pentagonal Number

The nth pentagonal figurate number.

Formula

Pn=n(3n−1)2P_n = \frac{n(3n-1)}{2}

Variables

nIndex

Example

P_3 = 12

Did You Know?

Pentagonal numbers surface unexpectedly in Euler's formula for counting the ways to add up whole numbers.

figurate