A. The sequence is not a direct variation.
B. There is no constant of variation.
D. The points do not lie on a line.
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.
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.
Sample Response: No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and its position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.
What did you include in your response? Check all that apply.
A.The sequence is not a direct variation.
B.There is no constant of variation.
C.The sequence cannot be described by the equation
y = kx.
D.The points do not lie on a line.
1 answer