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

a,b and c are in A.P. Prove that b+c , c+a and a+b are 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 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.