`1/a, 1/b and 1/c` are in A.P. Show that bc, ca, and ab are also in A.P.

If a,b and c are in A.P, show that (b+c), (c+a) and (a+b) are also in A.P.

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 are in A.P., show that: (b + c), (c + a) and (a + b) are also in A.P.

If a, b and c are in A.P. show that : (i) 4a, 4b and 4c are in A.P. (ii) a + 4, b + 4 and c + 4 are in A.P.

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

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 (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are also in A.P. (a +b+c != 0) .

If a, b, c are in A.P, then show that: b+c-a ,\ c+a-b ,\ a+b-c 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.

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.