The Nth triangular number is calculated by:
N(N + 1)
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2
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The formula for the nth triangular number is Tn = n(n+1)/2. To find the 1000th triangular number, we substitute n = 1000 into the formula: T1000 = 1000(1000+1)/2 = 1000(1001)/2 = 500500. Therefore, the 1000th triangular number is 500500.
0,1,3,6,10,15,21,28,36,45,55,66,78,91
Mass = Density x Volume
A triangular prism can be thought of as a stack of triangles. Then the volume is equal to the area of the triangular base multiplied by the height of the prism, or 1/2 length * width * height.
The formula for the nth triangular number is n(n+1)/2. If the 8th triangular number is 36, then we can set up the equation 8(8+1)/2 = 36. Solving for n, we get n = 7. Therefore, the 7th triangular number is 7(7+1)/2 = 28.