If `{a_n}` is a G.P. and `a_1=4`,r=5, find `a_6` and `S_6`.

In an AP :- given a = 5, d = 3, a_n = 50 find n and S_n .

Given a G.P. with a= 1, r= sqrt2 . Find S_20 .

In an AP :- given a_n = 4, d=2, S_n =-14, find n and a .

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.

If N_a= {a_n | n in N} , describe N_4 nn N_6 and N_3 nn N_5 .

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

Determine the number n in a geometric progression {a_n} , if a_1= 3, a_n= 96 and S_n= 189 .

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 ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

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) .