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

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.

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aksnkj aksnkj · Answer 2 · 2021-11-10T09:35:34+01:00

The triangular numbers can't be modeled in a mathematical formula because there is no evidence of some logic between the number of dots on a side and the triangular number.

Triangular numbers can be represented with equilateral triangles formed by dots.

Dots are used to form an equilateral triangle. For example, a side of an equilateral triangle has 3 dots. So, the total number of dots will be 6. Here, 6 is a triangular number.

So, the first five triangular numbers are 1, 3, 6, 10, and 15.

The triangular numbers don't follow any proper sequence or they can't be modeled in a mathematical formula because there is no evidence of some logic between the number of dots in a side and the triangular number.

Therefore, we can't define a direct variation between a triangular number and its position in the sequence.

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