Question

Let $T_n$ be the number of all possible triangles formed by joining vertices of an n-sided reqular polygon. If $T_{n+1}-T_n=10,$ then the value of $n$ is;

• A. 7
• B. 5
• C. 10
• D. 8

Answer 1

The correct option is B 5

We know,
$T_n={}^n{C}_3$ and $T_{n+1}={}^{n+1}{C}_3$
$T_{n+1}-T_n={}^{n+1}{C}_3{-}^n{C}_3=10$

$\Rightarrow {}^n{C}_2=10\Rightarrow n=5.$