If three positive numbers a, b, c are in A.P. and
`(1)/(a^(@)), (1)/(b^(2)),(1)/(c^(2))` also in A.P. , then

If three positive numbers a, b, c are in A.P. and 1/a^2,1/b^2,1/c^2 also in A.P. then

If three positive numbers a,b,c are in A.P ad tan^(-1)a,tan^(-1)b,tan^(-1)c are also in A.P such that b lt 1 and ac lt 1 then

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

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

If a, b, c are distinct real numbers such that a, b, c are in A.P. and a^2, b^2, c^2 are in H. P , then

If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) are also in A.P.

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

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

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

if a, b, c are in A.P., b, c, d are in G.P. and (1)/(c),(1)/(d),(1)/(e) are in A.P., then prove that a, c, e are in G.P.