Q:

What are triangular numbers?

A:

A triangular number is one that can be represented as a regular, triangle-shaped grid of equally spaced points having one element in the first row and an additional element in each row thereafter, according to Wolfram MathWorld. So the second row has two elements, the third row has three, etc.

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The first element in the first row represents the first triangular number. The three elements in the first two rows constitute the second triangular number. They are added to the three elements in the third row to obtain the next triangular number, which is six. Those six are added to the four points in the fourth row, resulting in a total of ten, which is the next triangular number. This same pattern continues to repeat itself so that the first twelve triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 and 78.

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