For all real a,b prove that `(a-b)^2,a^2 +b^2` and `(a+b)^2` are in A.P.

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

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

Prove that a - 5b, a - b and a + 3b are consecutive term of an A.P.

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 p ,q, r are in A.P., a is G.M. between p, q and b is G.M. between q, r, then prove that a^2, q^2, b^2 are in A.P.

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

If a+ib= (c+i)/(c-i) , where c is real, prove that a^2+b^2=1 and b/a= (2c)/(c^2-1) .

If a,b,c are in A.P. then :

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