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Triangular sequences

Triangular sequences

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The triangular sequence has first term of 1, second term of 1 + 2, third term of 1 + 2 + 3, and so on. This is called a triangular sequence because one can represent the sequence as a triangle of dots.

Basics of triangular sequences

The term to term rule is that the next term value is the current term + (the difference between the current term and previous term) + 1. Knowing this rule, you can generate further terms of the sequence just knowing 2 previous terms. Also, at position n, the term is the sum of the first n numbers 1 + 2 + … + n.

Terms in a triangular sequence

The nth term of the triangular sequence is the sum of the first n natural numbers 1 + … + n, which is equal to n(n+1)/2.

nth term of triangular sequences

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