If the sum pf first n , 2n , 3n , terms of an arithmetic progression be `S_(1)S_(2)andS_(1)` respectively , the prove that
`S_(3)=3(S_(2)-S_(1))`

If the sums of n, 2n and 3n terms of an A.P. be S_(1), S_(2), S_(3) respectively, then show that, S_(3) = 3(S_(2) - S_(1)) .

The nth term of an arithmetic progression is 3n-1. Find the progression.

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)

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

If s_1 ,s_2 and s_3 are the sum of first n,2n,3n terms respectively of an arithmetic progression, then show that s_3=3(s_2-s_1) .

If the first term, common ratio and the sum of first n terms of a G.P. be a, r and S_(n) respectively, find the value of S_(1) + S_(2) + S_(3) +….+S_(n) .

When a body is immersed separately into three liquids of specific gravities S_(1),S_(2)andS_(3) , its apparent weights become W_(1),W_(2)andW_(3) respectivley. Show that S_(1)(W_(2)-W_(3))+S_(2)(W_(3)-W_(1))+S_(3)(W_(1)-W_(2))=0 .

If S be the sum of first (2n+1) terms of an A.P and the sum of terms in odd positions of these (2n+1) terms be S', then show that (n+1)S = (2n+1)S'.

If S_1, S_2, S_3 are the sum of first n natural numbers, their squares and their cubes, respectively , show that 9 S_(2)^(2) = S_(3) (1+ 8S_1)

If S_1,S_2 and S_3 be respectively the sum of n, 2n and 3n terms of a G.P., prove that S_1(S_3-S_2)=((S_2)-(S_1))^2