Triangular Number Formula. The following formula can be used to calculate the triangular numbers: Tn = Σnk=1 k = 1 + 2 + 3 + 4…n = n (n+1)/2. In the above formula, (n+1)/2 is binomial coefficient. We know that sum of first 'n' natural numbers is given by n (n+1)/2. Hence, the sum of n natural numbers results in Triangular number.. It is simply the number of dots in each triangular pattern: By adding another row of dots and counting all the dots we can. find the next number of the sequence. The first triangle has just one dot. The second triangle has another row with 2 extra dots, making 1 + 2 = 3. The third triangle has another row with 3 extra dots, making 1 + 2 + 3 = 6.

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Knowing the triangle numbers, one can calculate any centered polygonal number; the nth centered k-gon number is obtained by the formula. Ckn = kTn − 1 + 1. Where T is a triangle number. The difference between the two triangular numbers is a trapezoidal number.. A triangular number correspond to the number of dots that would appear in an equilateral triangle when using a basic triangular pattern to build the triangule. The triangular numbers sequence contains all the triangular numbers in order. The first 10 numbers of the triangular number sequenceare: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,..