Question

Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6, 10, and 15. Is there a direct variation between a triangular number and its position in the sequence? Explain your reasoning.

Answer 1

nth triangular number = n* (n+1) / 2
Basically, input the triangular number's position in the sequence (for example four) then input the number position into the equation and you get the triangular number's value.
Example:
4 * (5/2) = 10
So, the 4th triangular number has a value of 10.

Answer 2

No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and its position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.

Hope this helps!!! :)