Let `S_(n)` be the sum to "n" -terms of an arithmetic progression `3,7,11,.......`If `40<((6)/(n(n+1))sum_(k=1)^(n)S_(k))<42`, then "n" equals____________

(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

Let S_(n) denote the sum of the first "n" terms of an arithmetic progression.If S_(10)=390 and the ratio of the tenth and the fifth terms is 15:7 ,then S_(15)-S_(5) is equal to:

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 S_(n) denote the sum of first n-terms of an arithmetic progression. If S_(10) = 530, S_(5) = 140 then S_(20) - S_(6) is equal to :

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_1 be the sum of first 2n terms of an arithmetic progression. Let S_2 be the sum first 4n terms of the same arithmeti progression. If (S_(2)-S_(1)) is 1000, then the sum of the first 6n term of the arithmetic progression is equal to :

If S_(n) denotes the sum of first n terms of an arithmetic progression and an denotes the n^(th) term of the same A.P.given S_(n)=n^(2)p; where p,n in N, then

Find the sum of n terms of the arithmetic- geometric sequence.