If sum of n termsof a sequende is `S_n` then its nth term `t_n=S_n-S_(n-1)`. This relation is vale for all `ngt-1` provided `S_0= 0.` But if `S_!=0`, then the relation is valid ony for `nge2` and in hat cast `t_1` can be obtained by the relation`t_1=S_1.` Also if nth term of a sequence `t_1=S_n-S_(n-1)` then sum of n term of the sequence can be obtained by putting `n=1,2,3,.n` and adding them. Thus `sum_(n=1)^n t_n=S_n-S_0.` if `S_0=0, then sum_(n=1)^n t_n=S_n.` On the basis of above information answer thefollowing questions:If nth term of a sequence is `n/(1+n^2+n^4)` then the sum of its first n terms is (A) `(n^2+n)/(1+n+n^2)` (B) `(n^2-n)/(1+n+n^2)` (C) `(n^2+n)/(1-n+n^2)` (D) `(n^2+n)/(2(1+n+n^2)`

If sum of n terms of a sequence is S_n then its nth term t_n=S_n-S_(n-1) . This relation is valid for all ngt-1 provided S_0= 0. But if S_1=0 , then the relation is valid only for nge2 and in hat cast t_1 can be obtained by the relation t_1=S_1. Also if nth term of a sequence t_1=S_n-S_(n-1) then sum of n term of the sequence can be obtained by putting n=1,2,3,.n and adding them. Thus sum_(n=1)^n t_n=S_n-S_0. if S_0=0, then sum_(n=1)^n t_n=S_n. On the basis of above information answer the following questions: If the sum of n terms of a sequence is 10n^2+7n then the sequence is (A) an A.P. having common difference 20 (B) an A.P. having common difference 7 (C) an A.P. having common difference 27 (D) not an A.P.

If the sum of n terms of sequence S_(n)=(n)/(n+1)

If sum of n terms of a sequence is given by S_(n)=3n^(2)-5n+7&t_(r) represents its r^(th) term then

Find the sum of nth term of this series and S_(n) denote the sum of its n terms.Then,T_(n)=[1+(n-1xx2)^(2)]=(2n-1)^(2)=4n^(2)-4n+1

If S_(n), be the sum of n terms of an A.P; the value of S_(n)-2S_(n-1)+S_(n-2), is

If S_(n) the sum of first n terms of an AP is given by 2n^(2)+n, then find its nth term.

For sequence (t_(n)), if S_(n)=5(2^(n)-1) then t_(n)= . . .

For the series sum t_(n,) S_n=sum_(n=1)^nt_n=2t_n-1 . Is the series geometric ? If so, find the sum to n terms of the series.

In a sequence, if S_n is the sum of n terms and S_(n-1) is the sum of (n-1) terms, then the nth term is _________.

The n t h term of an A.P., the sum of whose n terms is S_n , is S_n+S_(n-1) (b) S_n-S_(n-1) (c) S_n+S_(n+1) (d) S_n-S_(n+1)