If a+c = 2b and ab + cd + ad = 3bc, prove that the four numbers a, b, c, d are in A.P. `(b != 0)`.

If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (d-a) are in G.P.

If a, b, c, d are in H.P then ab + bc + cd =

If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.

Let a,b,c,d, be four quantities such that a+c=2 b and ab+cd+ad=3bc(b ne 0) . Prove that a,b,c and d are in A.P.

If (a + b) / (1- ab) , b, (b + c) / (1 - bc) are in A.P., then a, 1/b , c are in

If a, b, c are in A.P, prove that 1/(bc),1/(ca),1/(ab) are also in A.P.

If a^2 (b+c),b^2(c+a) , c^2(a+b) are in A.P., show that : either a, b, c are in A.P. or ab + bc + ca =0.

If a, b, d and p are distinct non - zero real numbers such that (a^2+b^2 + c^2) p^2 - 2(ab+bc+cd)p+(b^2 + c^2 +d^2) le 0 then n. Prove that a, b, c, d are in G. P and ad = bc

If a, b, c are in A.P., prove that : (bc)^-1,(ca)^-1 and (ab)^-1 are also in A.P.