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^2 + q^2 + r^2) (q^2 + r^2 + s^2) = (pq + qr + rs)^2

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. then show that (q -r )^(2) + ( r -p) ^(2) + ( s-q) ^(2) = ( p -s) ^(2)

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.

Find x if ^(n)P_r = x ^(n)C_r

Show that (n +1) ("^(n)P_r) = (n - r + 1) ["^((n +1))P_r]

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

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