Question

What type of number is obtained by adding two consecutive triangular numbers?

Answer 1

Consider the triangular numbers 1,3,6,10...
Adding the consecutive triangular numbers we get:
1+3=4
3+6=9
6+10=16

It is clear that the numbers 4,9,16 are square numbers as:
2$\times$2 = 4
3$\times$2 = 9
4$\times$2 = 16

So by adding two consecutive triangular numbers, a square number is obtained.