If a,b,c are in A.P. show that `bc-a^2,ca-b^2,ab-c^2` are also in A.P.

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

If a, b, c are in A.P., prove that : b+c,c+a,a+ b are also in A.P.

If a+b+c ne 0 and (b + c)/a, (c + a)/b, (a + b)/c are in A.P., prove that : 1/a,1/b,1/c 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 a, b, c are in A.P., prove that : (bc)^-1,(ca)^-1 and (ab)^-1 are also in A.P.

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.

If a,b,c are in A.P. and a^2,b^2,c^2 are in H.P. then which of the following could and true (A) -a/2, b, c are in G.P. (B) a=b=c (C) a^3,b^3,c^3 are in G.P. (D) none of these

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 the sum of the roots of the equation ax^2+bx +c = 0 is equal to the sum of the squares of their reciprocals, then show that bc^2, ca^2, ab^2 are in A.P.

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