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

A direct variation means proportionality. Triangular numbers are quadratic in n. T(n)=n(n+1)/2. So no.

Answer 2

direct variation is y = kx  where y  would be the value of the number and x would be its position in the sequence, k is a constant 

so for consecutive values y/x would be a constant k 

In this case its not true becuse for example  3/1 = 3 and 6/3 = 2 

so there is no direct variation here.