Each number represents the number of dots needed to form an equilateral triangle. To find the next number in the sequence, you simply add a new row of dots to the base of the previous triangle. 4. Apply the formula
To find any term without listing the whole sequence, plug the position into the explicit formula. For example, to find the 100th triangular number: Triangular Numbers 1, 3, 6, 10, 15 Non-Linear Pattern Rules
Triangular numbers are "non-linear" because the difference between terms is not constant. Instead, the difference increases by 1 each time. 2. Recognize the quadratic nature Each number represents the number of dots needed
Because the second difference is constant (always 1), the sequence is quadratic. This means the rule involves an n2n squared : Explicit Rule : 3. Visualize the geometry Triangular Numbers 1, 3, 6, 10, 15 Non-Linear Pattern Rules