If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.

If a, b and c are in A.P. a, x, b are in G.P. whereas b, y and c are also in G.P.

Show that : x², b², y² are in A.P.

Find the values of m and n, in each case; if :

(i) (4, -3) on reflection in x-axis gives (-m, n).

(ii) (m, 5) on reflection in y-axis gives (-5, n - 2)

(iii) (-6, n + 2) on reflection in origin gives (m + 3, -4).