For the A.P., `a_1, a_2,a_3,` ............., if `a_4/a_7= 2/3`, find `a_6/a_8`.

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) .

If the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

A sequence of numbers a_0,a_1,a_2,a_3 , ........ satisfies the relation a_n^2-a_(n-1)a_(n+1)=(-1)^n . Find a_3 , given a_0=1 and a_1=3 .

If a_1, a_2,a_3,..........., a_n are in A.P. with common difference d, prove that : sin d [cosec a_1 coseca_2+ coseca_2coseca_3+....coseca_(n-1)coseca_n]= cot a_1-a_n .

Given that : (a_1 + ib_1) (a_2 + ib_2) ... (a_n + ib_n) = c + id , show that : tan^-1 (b_1/a_1)+tan^-1 (b_2/a_2)+.............+ tan^-1 (b_n/a_n)= n pi+ tan^-1 (d/c) .

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If a_1, a_2 , ............, a_n are in A.P. and a_i >0 for all i , prove that : 1/(sqrt a_1+sqrt a_2)+1/(sqrt a_2+sqrt a_3)+.............+ 1/(sqrt (a_(n-1))+sqrt a_n)= (n-1)/(sqrt a_1+sqrt a_n) .

If a_1, a_2 , ............, a_n are in A.P.with common difference d ne 0 , then [sin d] [sec a_1 sec a_2 + sec a_2sec a_3+............+ sec a_(n-1) sec a_n] is equal to :

A person is to count 4500 currency notes, Let a_n denote the number of notes he courts in the nth minute. If a_1=a_2= ........ = a_10 =150 and a_10, a_11 , ............ are in an A.P. with common difference -2, then the time taken by him to count all notes is :

Let A and B be two sets such that n (A) = 5 and n(B) = 2. If (a_1, 2), (a_2, 3),(a_3,2), (a_4,3), (a_5,2) are in A xx B and a_1,a_2, a_3, a_4 and a_5 are distinct, find A and B.