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

@SolomonZelman @ganeshie8

Answer 2

direct variation relation :
\[\large y = kx\]

Answer 3

say \(x\) represents the position in the sequence

Answer 4

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

Answer 5

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.

Answer 6

Thank you so much !