If a, b, c, d are in GP, then prove that
`1/((a^(2)+b^(2))), 1/((b^(2)+c^(2))), 1/((c^(2)+d^(2)))` are in GP.

If a, b, c, d are in GP, prove that (a^(2)-b^(2)), (b^(2)-c^(2)), (c^(2)-d^(2)) are in GP.

If a, b, c are in GP, prove that (a^(2)+b^(2)), (ab+bc), (b^(2)+c^(2)) are in GP.

If a,b,c,d are in G.P.prove that: (i) quad (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P. (i) (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.

If a,b,c,d are in G.P.,prove that (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.and (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P

If a ,b ,a n dc are in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

If a,b,c,d are in G.P.prove that: (a^(2)+b^(2)),(b^(2)+c^(2)),(c^(2)+d^(2)) are in G.P.(a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.(1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.(a^(2)+b^(2)+c^(2)),(ab+bc+cd),(b^(2)+c^(2)+d^(2))

If a, b, c, d are in G.P., prove that a^(2) - b^(2), b^(2)-c^(2), c^(2)-d^(2) are also in G.P.

If a, b, c are in GP, prove that a^(2), b^(2), c^(2) are in GP.

If a, b, c are in G.P., then prove that (1)/(a^(2)-b^(2))-(1)/(b^(2)-c^(2))=-(1)/(b^(2)) . [Hint : Put b = ar, c = ar^(2) ]

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)