Suppose `a_1, a_2,...` are in AP and `S_k`, denotes the sum of the first `k` terms of this AP. If `S_n/S_m = n^4/m^4` for all `m, n in NN`, then prove that `a_(m+1)/a_(n+1) = (2m+1)^3/(2n+1)^3`

Let S_(n) denote the sum of first n terms of an AP and S_(2n) = 3S_(n) . If S_(3n) = k S_(n) , then the value of k is equal to

If a_(1),a_(2),...a_(k) are in A.P. then the equation (S_(m))/(S_(n))=(m^(2))/(n^(2)) (where S_(k) is the sum of the first k terms of the A.P) is satisfied . Prove that (a_(m))/(a_(n))=(2m-1)/(2n-1)

The sum of first n terms of an A.P. is S_n .If S_n=n^2p and S_m=m^2p(mnen) .Show that S_p=p^3 .

If S_(n) denotes the sum of first n terms of an A.P., then (S_(3n)-S_(n-1))/(S_(2n)-S_(n-1)) is equal to

If S_n denotes the sum of first n terms of an A.P. such that (S_m)/(S_n)=(m^2)/(n^2), t h e n(a_m)/(a_n)= a.(2m+1)/(2n+1) b. (2m-1)/(2n-1) c. (m-1)/(n-1) d. (m+1)/(n+1)

If S_(n) , denotes the sum of first n terms of a A.P. then (S_(3n)-S_(n-1))/(S_(2n)-S_(2n-1)) is always equal to

If S_n denotes the sum of first n terms of an A.P. such that (S_m)/(S_n)=(m^2)/(n^2),\ t h e n(a_m)/(a_n)= a. (2m+1)/(2n+1) b. (2m-1)/(2n-1) c. (m-1)/(n-1) d. (m+1)/(n+1)

S_(n) denots the sum of first n terms of an A.P. Its first term is a and common difference is d. If d= S_(n)-k S_(n-1) + S_(n-2) then k= ……….

In an A.P,the sum of m terms of an AP is n and sum of n terms of AP is m,then prove that sum of (m+n) terms of AP is-(m+n)

If the sum of the first m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, prove that, (m+n)((1)/(m)-(1)/(p)) = (m+p)((1)/(m) - (1)/(n))