You know that natural number series: 1,2,3,4,5,6,7,8,9….and so on.

Triangular number is the number obtained by adding all natural numbers less than or equal to given positive integer n or simply it can be said that in triangular number each term is obtained by adding the preceding number and the number itself

that is if the term is 5 then triangular number sequence of the term will be =preceding number+5=1+2+3+4+5=15

similarly ,for 4th term the sequence will be=1+2+3+4=10

The formula for finding the triangular number of nth term is :
if T(n) is triangular number of n th term then
T(n)=1+2+3+4…n=n(n+1)/2

for example for 5th term triangular number is T(5)=5*(5+1)/2=15

In the form of definition a triangular number is that number which can be represented in the form of triangular grid of dots/points in such a manner that each succeeding row consists of one element more than preceding one.
Every body has the knowledge of Square number so it is not required to discus here.