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

Step-by-step solution

A triangle can be formed from 3 vertices, so select 3 vertices out of x vertices. The number of ways of selecting 3 vertices out of n is ^n C₃ . array ll & T_ n+1 -T_n=10 & ^ n+1 C₃- ^n C₃=10 & ^n C₂=10 [ ^n C_r+ ^n C_ r+1 = n+1 r+1 ] & n(n-1) 2 =10 n^2-n-20=0 & n^2-5 n+4 n-20=0 & n(n-5)+4(n-5)=0 & (n-5)(n+4)=0 n=5, n -4 array