Question

If a,b,c,d are in A.P thn prove thy 1/bc,1/ca,1/ab are also in A.P

Answer 1

If a,b,c,d are in AP then their common difference would be same
b-a=c-b          point as 1
According to question
1/bc,1/ca,1/ab
let us check thei  difference if their will have common difference then they will definately in Ap
1/ca-1/bc⇒bc-ca         
                   abc²

b-a
abc
1/ab-1/ca
c-b
abc

from eq 1 b-a
               abc
they have common ratio.hence these terms are also in AP