This leads them to see that the 10th triangular number is the 4th triangular number plus 5 + 6 + 7 + 8 + 9 + 10. That is, 10 + 5 + 6 + 7 + 8 + 9 + 10. These can be added in order to give the 10th triangular number as 55.

Why is 10 a triangular number?

Triangular numbers are numbers that make up the sequence 1, 3, 6, 10, . . .. The nth triangular number in the sequence is the number of dots it would take to make an equilateral triangle with n dots on each side.

How many dots are in the 10th triangular number?

It is 1 + 2 + 3 + 4 + + n = n(n + 1)/2. So, in this case, the number of dots in Figure 10, which represents the tenth Triangular Number, is 10(11)/2 = 110/2 = 55 dots.