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Let Tₙ represent the count of triangles that can be formed from the vertices of a regular polygon with n sides. If Tₙ₊₁ - Tₙ = 28, then the value of n is

1. 4
2. 5
3. 6
4. 8

Correct answer: 8

Solution

T_n = C(n,3). T_(n+1)-T_n = C(n+1,3)-C(n,3) = C(n,2) = n(n-1)/2 = 28 -> n^2-n-56=0 -> n=8.

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