The non-linear pattern of triangular numbers is defined by the rule that the -th triangular number ( Tncap T sub n ) is the sum of the first natural numbers, which simplifies to the quadratic formula Licensed by Google 1. Identify the constant difference
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
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 The non-linear pattern of triangular numbers is defined
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 This means the rule involves an n2n squared