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), denotes the sum of n terms of an AP, then the value of (S_(2n)-S_(n)) is equal to

If S_(n), denotes the sum of n terms of an A.P. then S_(n+3)-3S_(n+2)+3S_(n+1)-S_(n)=

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) is the sum of the first n terms of an A.P. then : (a) S_(3n)=3(S_(2n)-S_n) (b) S_(3n)=S_n+S_(2n) (c) S_(3n)=2(S_(2n)-S_(n) (d) none of these

Let S_(n) be the sum of n terms of an A.P. Let us define a_(n)=(S_(3n))/(S_(2n)-S_(n)) then sum_(r=1)^(oo)(a_(r))/(2^(r-1)) is

If S_(n) denotes the sum of first n terms of an AP, then prove that S_(12)=3(S_(8)-S_(4)).

If S_r denotes the sum of the first r terms of an A.P. Then, S_(3n)\ :(S_(2n)-S_n) is n (b) 3n (c) 3 (d) none of these

If S_(n) denotes the sum of n terms of A.P.then S_(n+1)-3S_(n+2)+3S_(n+1)-S_(n)=2^(S)-nbs_(n+1)c.3S_(n)d.0