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

If S is the sum, P the product and R the sum of reciprocals of n terms of a G.P., then prove that P^2 = (S/R)^n .

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

If S_(1) , S_(2) and S_(3) are the sums of first n natural numbers, their squares and their cubes respectively then show that - 9 S_(2) ^(2) = S _(3) (1 + 8 S _(1))

Two hollow concentric spheres S_1 and S_2 enclosing charges 2Q and 6Q respectively, as shown in figure:- What is the ratio of electric flux through S_1 , and S_2 ? '(##CHT_MK_AJI_PHY_XII_P1_C03_S01_018_Q01##)'

If a = 1, r = 2 find S _(n) for the G. P.

Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. TI1eir periods of revolution are 2 hours and 16 hours respectively. If the radius of the orbit of S_1 is 10^4 , then the radius of the orbit of S_2 is

For a G.P. If a = 1, r = -3/2 , find S_5

If p, q, r, s are in G.P. then show that (q -r )^(2) + ( r -p) ^(2) + ( s-q) ^(2) = ( p -s) ^(2)