Question

If a;b;c are in A.P then prove that 1/bc;1/ac;1/ab are also in A.P

Answer 1

If a,b,c are in ap, then
their common difference would be:
b – a and c-b
and therfore,
2b = a+c..................(1)
If
1/ba, 1/ca, 1/cb are in A.P,
then
2/ca = 1/ba + 1/cb
taking L.C.M abc and calculating we get,
again
2b = a + c.................(2)
hence eqn. (1) and (2) are similar therefore this series is also in A.P.
if abc are in ap , then cba are in AP which means

Answer 2

prove it out by the common difference method