contestada

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?

Respuesta :

As observed in the given triangular numbers, 1, 3, 6, 10, and 15, the first two differ by 2. The second and the third, differ by 3. The third and fourth differ by 4 and the last two differ by 5. From this, it can be concluded that the difference between the triangular numbers from an arithmetic sequence with 2 as the first term and common difference of 1. 
jennacope

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.