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

the first triangular number is 1
we can think of this as a coordinate point (1,1)

the second triangular number is 3
we can assign this as (2,3)

following this logic, we get (1,1), (2,3), (3,6), (4,10) and (5,15) as our x and y values.

now, can you write an equation such that y = kx for constant k, that works for *all* of the (x,y) values?