If `s_(1),s_(2)and s_(3)` are the sum of first n , 2n, 3n terms respectively of an arithmetical progression , then show that `s_(3)=3 (s_(2)-s_(1))`

If S_(1), S_(2), S_(3) are the sums of n, 2n, 3n terms respectively of an A.P., then S_(3)//(S_(2) - S_(1))-

If S_(n)=n^(2)a+(n)/(4)(n-1)d is the sum of the first n terms of an arithmetic progression, then the common difference is

If S_1, S_2, S_3 are the sums to n, 2n, 3n terms respectively for a GP then prove that S_1,S_2-S_1,S_3-S_2 are in GP.

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 :

{:("List-I","List-II"),((P)"A geometirc progression consists of an even" ,(1)7),("number of terms. if the sum of all the terms is",),("then its common ratio is",),((Q)Let S_(n).S_(2n).S_(3n)"be the sums of first n.2n.3n",(2)4),((n in N)"terms of an arithmetic progression then",),((S_(3n))/(S_(2n)-S_(n)) "is equal to",),((R)"Number of ordered pairs (a.b)where a.b" in N,(3)3),("such that" 6.a.b ("taken in that order") "are in harmonic progression is equal to",):}

If S_(1),S_(2)andS_(3) denote the sum of first n_(1)n_(2)andn_(3) terms respectively of an A.P., then (S_(1))/(n_(1))(n_(2)-n_(3))+(S_(2))/(n_(2))+(n_(3)-n_(1))+(S_(3))/(n_(3))(n_(1)-n_(2)) =

Let S_(1),S_(2),S_(3) be the respective sums of first n,2n and 3n terms of the same arithmetic progression with a as the first term and d as the common difference.If R=S_(3)-S_(2)-S_(1) then R depends on

If the sum of 'n' terms of an arithmetic progression is S_(n)=3n +2n^(2) then its common difference is :

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 :