Question

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

• A. 5
• B. 10
• C. 8
• D. 7

Answer 1

The correct option is A 5

we know that a triangle needs $3$ vertices to be formed so out of $n$ vertices $3$ should be chosen$={}^n{C}_3$

According to the given condition, we can write that

${}^{n+1}{C}_3{-}^n{C}_3=10$

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

$\Rightarrow n=5$