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 (1) 5 (2) 10 (3) 8 (4) 7

Options

A. 5
B. 10
C. 8
D. 7

Answer

A

Explanation

`because T_(n+1)-T_(n)=10 implies.^(n+1)C_(3)-.^(n)C_(3)=10implies.^(n)C_(2)=.^(n)C_(3)-.^(n)C_(3)=10`
`implies.^(n)C_(2)=10=(20)/(2)=(5*4)/(1*2)=.^(5)C_(2)impliesn=5`