Triangular numbers are those numbers which can be represented by the dots in the sides of an equilateral triangle.
In general a triangular number is the additive sum given by Tn= 1+2+3+4+……..+n.
Thus T1 =1, T2 = 1+2, T3= 1+2+3, T4= 1+2+3+4, T5= 1+2+3+4+5, T6 = !+2+3+4+5+6..
It is seen that T5 is 15 and T6 = 21. This can be represented by the dots on an equilateral triangle as follows:
***