Let `S_(n)` denote the sum of first n terms of the sequences` 1,5,14,30 ,55………..` then prove that `S_(n)-S_(n-1)=Sigman^(2)`

If S_(n) denotes the sum of first n terms of an AP, then prove that S_(12)=3(S_(8)-S_(4)).

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.

Let S_n denotes the sum of the first of n terms of A.P. and S_(2n)=3S_n . then the ratio S_(3n):S_n is equal to

Let S_n denote the sum of first n terms of an A.P. If S_(2n)=3S_n , then find the ratio S_(3n)//S_ndot

Let S_n denote the sum of first n terms of an A.P. If S_(2n)=3S_n , then find the ratio S_(3n)//S_ndot

Let S_n denote the sum of first n terms of an A.P. and S_2n = 3S_n then ratio of S_3n : S_n

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 first n terms of an A.P., prove that S_(12)=3(S_8-S_4) .

If S_(n) denote the sum to n terms of an A.P. whose first term is a and common differnece is d , then S_(n) - 2S_(n-1) + S_(n-2) is equal to

Let S be the sum of the first n terms of the arithmetic sequence 3, 7, 11, ...., and let T be the sum of the first n terms of the arithmetic sequence 8 , 10 , 12 ,.... For n gt 1 , S = T for