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 it’s position in the sequence? Explain your reasoning

Answer 1

The sequence is not a direct variation.

There is no constant of variation.

The sequence cannot be described by the equation

y = kx.

The points do not lie on a line.

Step-by-step explanation:

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Answer 2

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.