[a,b,c" are also in "nP],[(9)/(b+c)" ,"(b)/(a+c)" at "b" are in "]

If a, b, c are in A.P., then prove that : (i) b+c,c+a,a+b" are also in A.P." (ii) (1)/(bc),(1)/(ca),(1)/(ab)" are also in A.P." (iii) (a(b+c))/(bc),(b(c+a))/(ca),(c(a+b))/(ab)" are also in A.P."

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

If a, b, c are in H.P., prove that (a)/(b+c), (b)/(c+a) and (c )/(a+b) are also in H.P.

If a,b,c are in H.P. show that a/(b+c),b/(c+a),c/(a+b) are also in H.P.

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

If a,b,c are in AP, show that (a(b+c))/(bc) , (b (c+a))/(ca), (c(a+b))/(ab) , are also in AP.

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