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.

Accepted Solution

Answer:Yes, those are the first triangular numbers.There is a relation between the number and its position but isn't direct. Step-by-step explanation:The triangular numbers can be represented by equilateral triangles, but also can be represented by:[tex]T_{n} = \frac{n(n+1)}{2}[/tex] where:n, represents the position T represent the triangular number.As you may see, the equation of triangular numbers is not a straight line. It is a parable. For that reason there isn't a direct variation.