If `S_(n)` denotes the sum of n terms of a G.P., then show that `(S_(10)-S_(20))^(2)=S_(10)(S_(30)-S_(20))`

If S_(n) denotes the sum of n terms of a G.P., prove that: (S_(10)-S_(20))^(2)=S_(10)(S_(30)-S_(20))

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_(n) denotes the sum of the first n terms of an A.P.prove that S_(30)=3(S_(20)-S_(10)).

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.prove that S_(12)=3(S_(8)-S_(4))

If S_(1),S_(2),S_(3) be respectively the sums of n,2n,3n terms of a G.P.,then prove that S_(1)^(2)+S_(2)^(2)=S_(1)(S_(2)+S_(3))

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 A.P.then S_(n+1)-3S_(n+2)+3S_(n+1)-S_(n)=2^(S)-nbs_(n+1)c.3S_(n)d.0

If S_(k) denotes the sum of first k terms of a G.P. Then, S_(n),S_(2n)-S_(n),S_(3n)-S_(2n) are in

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