If p, q, r, s are in G.P, show that `(p^2 + q^2 + r^2) (q^2 + r^2 + s^2) = (pq + qr + rs)^2`

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

If p, q, r, s are in G.P, show that (p^n + q^n) , (q^n + r^n) , (r^n + s^n) are also in G.P

If p,q,r,s are in G.P. show that (p+q),(q+r),(r+s) are also in G.P.

If p, q, r, are in G.P. and p^(1/x) = q^(1/y) = r^(1/z) Verify x, y, z are in A.P or G.P or neither.

(~ p ^^ ~ q) ^^ ( q ^^ r) is a

If p,q, r are in G. P. and p ^( 1//x) = q ^( 1//y)= r ^( 1//z), verify whether x,y,z are in A.P. or G. P. or neither.

If x, y and z are the pth, qth, and rth, terms of a G.P respectively, then show that x^(q-r) . y^(r-p) . z^(p-q) = 1.

For the following G.P.'s find S_n p, q, q^2 / p , q^3 / p^2 , ………...