If the sum of n, 2n, 3n terms of an A.P are `S_(1), S_(2), S_(3)`, respectively, prove that `S_(3) = 3 (S_(2) -S_(1)).`

Let the sum of n, 2n, 3n terms of an A.P. be S_(1), S_(2) and S_(3) respectively. Show that S_(3) = 3(S_(2) - S_(1)) .

If the sum of n , 2n , 3n terms of an AP are S_1,S_2,S_3 respectively . Prove that S_3=3(S_2-S_1)

The sum of n ,2n ,3n terms of an A.P. are S_1S_2, S_3, respectively. Prove that S_3=3(S_2-S_1)dot

Let the sum of n, 2n, 3n terms of an A.P. be S_1,S_2 and S_3 , respectively, show that S_3=3(S_2-S_1) .

If the sum of n, 2n and infinite terms of G.P. are S_(1),S_(2) and S respectively, then prove that S_(1)(S_(1)-S)=S(S_(1)-S_(2)).

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

The sum of terms of a G.P if a_(1)=3,a_(n)=96 and S_(n)=189 is

If S_(1),S_(2),S_(3) be respectively the sum of n, 2n and 3n terms of a GP, then (S_(1)(S_(3)-S_(2)))/((S_(2)-S_(1))^(2)) is equal to

Let S_n denote the sum of the first n tem of an A.P. If S_(2n)=3S_n then prove that (S_(3n))/(S_n) =6.

If S_(1),S_(2), S_(3),......, S_(p) are the sums of infinite geometric series whose first terms are 1, 2, 3..... p and whose common ratios are (1)/(2),(1)/(3),.... (1)/(p+1) respectively, prove that S_(1) +S_(2)+S_(3)+.... + S_(p) = (1)/(2) p (p+3) .