The equation of given line is $1 x + my + n =0...(1)$
If $1, m, n$ are in arithmetic progression then, $2 m=1+n...(2)$
Equation (2) can be written as,
$1-2 m +n=0...s(3)$
Now comparing the equation (3) with equation (1),
we can clearly see that line $1 x +$ my $+n=0$
passes through the point $(1,-2)$