If a,b,c are in A.P. prove that `b+c,c+a,a+b ` are also 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. prove that the following are also in A.P. b+c, c+a, a+b

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)

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

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

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 ,c are in A.P., prove that the following are also in A.P. (i) 1/(b c),1/(c a),1/(a b), (ii) b+c ,c+a ,a+b (iii) a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) (iv) a^2(b+c),b^2(c+a),c^2(a+b) (v) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

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