Pyramidal Numbers

Pyramidal Numbers:
A pyramidal number is a figurate number that represents a pyramid with a base and a given number of sides.
This term is most often used to refer to square pyramid numbers which has four sides but it can also be used to refer to:
1)Tringlular pyramidal numbers(three sides)
2)Square Pyramidal numbers(four sides)
3)Pentagonal Pyramidal numbers(five sides)
4)Hexagonal Pyramidal numbers(six sides)
5)Heptagonal Pyramidal numbers(seven sides)

1)Tringular pyramidal number:
=>It is known as tetrahedral pyramidal numbers.
First few tetrahedral numbers are:
1,4,10,20,35....
Formula to represent Tetrahedral numbers is:
=>T_n=n(n+1)(n+2)/6
It can also be given as:_(n+2)C₃











2)Square Pyrmidal number:
=>Square Pyramidal or simply pyramid number is a figurate number which represents number of stacked spheres in a pyramid wi square phase.
Few Square Pyramidal numbers are:
1,5,14,30,55........
Formula that represents Square Pyramidal numbers:
T_n = ΣK² (where k is from 1 to n)

3)Pentagonal Pyramidal Numbers:
=>Is a figurate number which represents the number of objects in a pyramid with pentagonal base.
Few Pentagonal Pyramidal Numbers are:
1,6,18,40,75.........
formula: n²(n+1)/2