Find the number of all three elements subsets of the set`{a_1, a_2, a_3, ........... a_n}` which contain `a_3dot`

The number of all three element subsets of the {a_1,a_2 ,a_3 ,… a_n} which contain a_3 is

The number all three element ofsubsets of the set A = {a_1 ,a_2 , . . . A_8} contains the element a_3 is

If one quarter of all three element subsets of the set A = { a_1 ,a_2,a_3,. . . ,a_n} contains the element a_3 then n=

FOr an integer nlt2, we have real numbers a_1,a_2,a_3,a_4,..........,a_n such that a_2+a_3+a_4+.......+a_n=a1 and a_1+a_3+a_4+...........+a_n=a_2...............a_1+a_2+a_3+..............+a_(n-1)=a_n what is the value of a_1+a_2+a_3+........+a_n?

Find the terms indicated in the following case : a_n =(n-1)(2-n) (3+n), a_1, a_2, a_3 .

If a_1, a_2,a_3,..........., a_n be an A.P. of non-zero terms, prove that : 1/(a_1 a_2)+1/(a_2 a_3)+ ............. + 1/(a_(n-1) a_n)= (n-1)/(a_1 a_n) .

Let a_1=0 and a_1,a_2,a_3 …. , a_n be real numbers such that |a_i|=|a_(i-1) + 1| for all I then the A.M. Of the number a_1,a_2 ,a_3 …., a_n has the value A where : (a) A lt -1/2 (b) A lt -1 (c) A ge -1/2 (d) A=-2