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If $T_n$ denotes no. of triangles formed by the vertices of a regular $n$ sided polygon and if $T_{n+1}-T_n=21$, then $n=?$

$\begin{array}{1 1} 4 \\ 5 \\ 6\\ 7 \end{array}$

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Since 3 points are reguired to form a triangle,
no. of $\Delta^s$ using $n$ points (vertices of the polygon) = $T_n=^nC_3$
$\Rightarrow\:n=7\:or\:-6$ (which is not possible)
answered Aug 13, 2013 by rvidyagovindarajan_1

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