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.
If a,b,c are in AP it follows that
……..(1)
and a,x,b and b,y,c are in individual GPs which follows
…….(2)
……..(3)
Adding eqn 2 and 3 we get,
which shows are in AP.