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

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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y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct