Discussion Forum

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

Answer:

Explanation:

Given ,   $T_{n}=^{n}C_{3}$

   $T_{n+1}=^{n+1}C_{3}$

 $\therefore$     $T_{n+1}-T_{n}=^{n+1}C_{3}-^{n}C_{3}=10(given)$

  $\Rightarrow $    $^{n}C_{2}+^{n}C_{3}-^{n}C_{3}=10$

                                        $(\because ^{n}C_{r}+^{n}C_{r+1}=^{n+1}C_{r+1})$

  $\Rightarrow $    $ ^{n}C_{2}=10\Rightarrow n=5$