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:

 

                                

                                                        

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