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.

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 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, 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)

For the G.P. If r = (1)/(3), a = 9 find t _(7)

For the following G.P. s, find S _(n) p, q, ( q ^(2))/( p) , ( q ^(3))/( p) ,...

If z=x+iy and z^(1/3) = p+iq, then (x/p+y/q) ÷ ( p^2 - q^2 )=