Let `S_(n)` be the average of the multiples of `n` between `1` and `101,` and `n in{2,3,4,5,6}` .Find the value of `n` such that `S_(n)` is the largest.

There are 'n' A.M.'s between 2 and 41. The ratio of 4th and (n - 1)th mean is 2 : 5, find the value of n.

Let S_(n) be the sum of first n terms of and A.P. If S_(3n)=5S_(n) , then find the value of (S_(5n))/(S_(n)) is.

Let S_(n) be the sum of the first n terms of an arithmetic progression .If S_(3n)=3S_(2n) , then the value of (S_(4n))/(S_(2n)) is :

Let a_n be the n^(th) term of an arithmetic progression. Let S_(n) be the sum of the first n terms of the arithmetic progression with a_1=1 and a_3=3_(a_8) . Find the largest possible value of S_n .

Let S(n) denotes the number of ordered pairs (x,y) satisfying 1/x+1/y=1/n, " where " n gt 1 " and " x,y,n in N . " " (i) Find the value of S(6). " " (ii) Show that, if n is prime, then S(n)=3, always.

If S_(3n)=2S_n then find the value of S_(4n)/S_(2n)

(1) .Let S_n denote the sum of the first 'n' terms and S_(2n)= 3S_n. Then, the ratio S_(3n):S_n is: (2) let S_1(n) be the sum of the first n terms arithmetic progression 8, 12, 16,..... and S_2(n) be the sum of the first n terms of arithmatic progression 17, 19, 21,....... if S_1(n)=S_2(n) then this common sum is