If `(b+c-a)/a, (c+a-b)/b,(a+b-c)/c` are in A.P., show that `1/a,1/b,1/c` are in A.P. provided `a+b+c !=0`

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 inA.P

if ((b +c -a))/a,((c+a -b))/b, (( a+b -c))/c are in AP, prove that 1/a , 1/b,1/c are in AP.

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 in A.P.

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

If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

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

If a,b,c are in A.P. then

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

If (b+c-2a)/(a) , (c+a-2b)/(b),(a+b-2c)/(a) are in A.P then show that (1)/(a),(1)/(b),(1)/(c ) are also in A.P