Question

If $a^2,b^2,c^2$ are in A.P., then the following are also in A.P.
$\frac{1}{b+c},\frac{1}{c+a},\frac{1}{a+b}$.

Answer 1

$\frac{1}{c+a}-\frac{1}{b+c}=\frac{1}{a+b}-\frac{1}{c+a}$ or $\frac{b-a}{b+c}=\frac{c-b}{a+b}$

or $b^2-a^2=c^2-b^2$ or $2b^2=a^2+c^2$