Question

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.

Answer 1

a, b and c are in A.P.

`=>` 2b = a + c

a, x and b are in G.P.

`=>` x² = ab

b, y and c are in G.P.

`=>` y² = bc

Now,

x² + y² = ab + bc

= b(a + c)

= b × 2b

= 2b²

`=>` x², b² and y² are in A.P.