If $T_n$ denotes the number of triangles which can be formed using the vertices of regular polygon of…
If $T_n$ denotes the number of triangles which can be formed using the vertices of regular polygon of $\mathrm{n}$ sides and $\mathrm{T}_{\mathrm{n}+1}-\mathrm{T}_{\mathrm{n}}=21$, then $\mathrm{n}=$
5
7
6
4
Solution
According to the given condition, $\mathrm{T}_{\mathrm{n}}={ }^{\mathrm{n}} \mathrm{C}_3$
$\therefore \quad \mathrm{T}_{\mathrm{n}+1}-\mathrm{T}_{\mathrm{n}}=21 \Rightarrow{ }^{\mathrm{n}+1} \mathrm{C}_3-{ }^{\mathrm{n}} \mathrm{C}_3=21$
Note that $\mathrm{n}=7$ satisfies the above condition.
$\therefore \quad$ Option (B) is correct.