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 : $x^{2}, b^{2}, y^{2}$ are in A.P.

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Solution

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.

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