T_m denotes the number of triangles that can be formed with the vertices of a regular polygon of m sides. If T_ m+1 -T_m=15 , then m is equal to

Step-by-step solution

Given, T_m= Number of triangles formed with the vertices of a polygon of m sides. Also, T_ m+1 -T_m=15 As we know, ^n C_r+ ^n C_ r+1 = n+1 r+1 ^m C₂+ ^m C₃= m+1 2+1 ^m C₂+ ^m C₃=15+ ^m C₃ [from eq. (i) ] aligned & ^m C₂=15 & m ! 2 !(m-2) ! =15 & m(m-1)=30 & m^2-m-30=0 & (m-6)(m+5)=0 & m=6-5 aligned m=6 [ m -5]