Yes, there is a direct variation between a triangular number and its position in the sequence.
The nth triangular number can be calculated using the formula Tn = n(n+1) / 2, where n represents the position in the sequence.
For example, the 4th triangular number can be calculated by plugging in n=4 into the formula: T4 = 4(4+1) / 2 = 10.
As seen in the above example, the triangular number increases as the position in the sequence increases by a constant rate according to the formula. Therefore, there is a direct variation between a triangular number and its position in the sequence.
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.
_____________________
1 answer