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

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

As_(2)S_(3) sol is ,

Let S_n denote the sum of first n terms of an AP and 3S_n=S_(2n) What is S_(3n):S_n equal to? What is S_(3n):S_(2n) equal to?

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 for a sequence {a_(n)},S_(n)=2n^(2)+9n , where S_(n) is the sum of n terms, the value of a_(20) is

Consider an AP with a as the first term and d is the common difference such that S_(n) denotes the sum to n terms and a_(n) denotes the nth term of the AP. Given that for some m, n inN,(S_(m))/(S_(n))=(m^(2))/(n^(2))(nen) . Statement 1 d=2a because Statement 2 (a_(m))/(a_(n))=(2m+1)/(2n+1) .

Show that S_(n)=(n(2n^(2)+9n+13))/(24) .

Find as indicated in the following case : S_(n)=S_(n-1)-1,(ngt2), S_(1)=S_(2)=2,S_(5) .

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) .