Question

Why 1 is called as triangular number.

Answer 1

These are the first 100 triangular numbers:

The sequence of the triangular numbers comes from the natural numbers (and zero), if you always add the next number:

1
1+2=3
(1+2)+3=6
(1+2+3)+4=10
(1+2+3+4)+5=15
...

You can illustrate the name triangular number by the following drawing:

The general representation of a triangular number is d_n= 1 + 2 + 3 + 4 +...+ (n-2) + (n-1) + n,
where n is a natural number.