If `S_1` be the sum of `(2n+1)` term of an A.P. and `S_2` be the sum of its odd terms then prove that `S_1: S_2=(2n+1):(n+1)dot`

If s_1 be the sum of (2n+1) terms of an A.P and s_2 be the sum its odd terms, then prove that s_1:s_2=(2n+1):(n+1)

If the sum of first n,2n,3n terms of an A.P. be S_1 , S_2 and S_3 respectively then prove that S_1+S_3=2S_2

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

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 denotes the sum of an infinite G.P. adn S_1 denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively (2S S_1)/(S^2+S_1)a n d(S^2-S_1)/(S^2+S_1) .

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)

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

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)