Question

If $a,b,c$ are in A.P. then prove that $\frac{1}{bc},\frac{1}{ca},\frac{1}{ab}$ are also in A.P

Answer 1

It is given that $a,b,c$ are in A.P.

Divide each term by $abc$, so we get,

$\frac{a}{abc},\frac{b}{abc},\frac{c}{abc}$ are also in A.P

Now by simplifying we get,

$\frac{1}{bc},\frac{1}{ac},\frac{1}{ab}$ are in A.P

Hence proved.