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

for a direct variation, you can write it in the form y = kx, where k is a constant

treat the triangular numbers as x,y coordinates (1,1), (2,3), (3,6), etc.

take one coordinate value (ex: (1,1)) and plug it into y = kx and calculate the k

repeat this process with the other coordinate values

if the variation is direct, you should get the same k value each time. if you have *any* k values that are different, that means k is not a constant and thus the variation is not direct.