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

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.

Answer 2

Answer:

No, there is NOT a direct variation.

Step-by-step explanation:

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.