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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.

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Edufirst

position in the sequence    triangular number    relation

1                                          1                              1 = 1*(1+1)/2

2                                          3                              3 = 2(2+1)/2

3                                          6                              6 = 3(3+1)/2

4                                         10                            10 = 4(4+1)/2

5                                         15                              15= 5(5+1)/2

Call n the position in the sequence, then the triangular number is: n(n+1)/2
 

direct variation is y = kx  where y  would be the value of the number and x would be its position in the sequence, k is a constant 


so for consecutive values y/x would be a constant k 

In this case its not true becuse for example  3/1 = 3 and 6/3 = 2 


so there is no direct variation here.



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