If a,b,c, d are in G.P., show that :
`a^(2)+b^(2), b^(2)+ c^(2)` and `c^(2)+d^(2)` are also in G.P.

If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (c^(n) + d^(n)) are in G.P.

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

If a, b, c and d are in G.P. show that (a^2+ b^2+ c^2) (b^2 + c^2 + d^2)= ( ab + bc + cd)^2 .

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2) .

If a,b,c are in AP, than show that a^(2)(b+c)+b^(2)(c+a)+c^(2)(a+b)=(2)/(9)(a+b+c)^(3) .

If a, b, c are in A.P., prove that : (b+c)^2-a^2, (c+a)^2-b^2, (a+b)^2-c^2 are also in A.P.

If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+2ex+f=0 have a common root if a/d,b/e,c/f are in

If b^2+c^2, c^2+a^2, a^2+b^2 are in A.P. prove that : 1/(b + c), 1/(c + a), 1/(a + b) are also in A.P.

If (a+ib)/(c+id)=x + iy , show that : x^2+y^2= (a^2+b^2)/(c^2 +d^2) .