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.

Question

anonymous · Answer

@SolomonZelman @ganeshie8

ganeshie8 · Answer

direct variation relation :
$$\large   y = kx$$

ganeshie8 · Answer

say $x$ represents the position in the sequence

ganeshie8 · Answer

then the first triangular should be obtained by : 
$$\large 1 = k*1 \implies k = 1$$

ganeshie8 · Answer

so  $\large y = x$ has to be the direct variation relation

however clearly you cannot obtain other triangular numbers using this relation. so the triangular numbers cannot form a direct variation realtion.

anonymous · Answer

Thank you so much !