Question

Write 121 as sum of two consecutive triangular numbers.

Answer 1

Let's first write some triangular number,
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78 ......
If we add two consecutive triangular numbers, we get a square number, like
Adding 1 and 3, first and second triangular numbers, we get,
1 + 3 = 4, which is second square number.

Similarly, adding 3 and 6, second and third triangular numbers, we get,
3 + 6 = 9, which is third square number.

We can write 121 as ${11}^2$,
It means 121 is eleventh square number
So, for eleventh square number we will be adding 10th and 11th triangular number. which are 55 and 66
Therefore, 121 = 55 + 66.