Calculate the n-th triangular number
A triangular number counts objects arranged in an equilateral triangle. The n-th triangular number is the sum of the first n natural numbers.Tₙ = n(n + 1) / 2
Decide which triangular number you want: first (n=1), second (n=2), etc.
Why: The term number n defines which triangular number to calculate. n=1 gives 1, n=2 gives 3, n=3 gives 6, etc.
Recognize that Tₙ = 1+2+3+...+n (sum of first n natural numbers).
Why: The pattern helps visualize why the result looks triangular. It shows the recursive nature of triangular numbers.
Confirm n ≥ 0 and is a whole number (no decimals).
Why: Triangular numbers are only defined for non-negative integers. Fractional n doesn't produce counting numbers.
Calculate Tₙ = n(n+1)/2
Why: This formula comes from the arithmetic series sum. It avoids adding all terms individually.
Cross-check by adding: 1+2+3+...+n should equal the formula result.
Why: This verification confirms the formula application. For small n, direct summation is quick to verify against.
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