Triangular Numbers Calculator

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Forward: give n, get T(n). Reverse: give a triangular number, get n.
A non-negative integer. T(7) = 28, for example.
How many consecutive triangular numbers to list starting from n (forward mode only).
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Triangular number T(n)
28

The nth triangular number: sum of 1 + 2 + ... + n

Position n7
Sum of first n integers28
Previous T(n-1)21
Next T(n+1)36
Square relation: T(n) + T(n-1)49
T(n-1)21
T(n)28
T(n+1)36

T(7) = 28

  • T(7) = 7 x (7 + 1) / 2 = 7 x 8 / 2 = 28.
  • T(7) + T(6) = 28 + 21 = 49, confirming that two consecutive triangular numbers sum to n^2.
  • The 7th triangular number represents a triangle with 7 dots on each side - imagine stacking 1 ball, then 2, then 3, up to 7 in a triangular pile.

Next stepTo find the next triangular number, add 8 to 28: T(8) = 36.

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