  We study the arithmetic (geometric) progressions in the $x$-coordinates of
quadratic points on smooth projective planar curves defined over a number field
$k$. Unless the curve is hyperelliptic, we prove that these progressions must
be finite. We, moreover, show that the arithmetic gonality of the curve
determines the infinitude of these progressions in the set of
$\overline{k}$-points with field of definition of degree at most $n$, $n\ge 3$.
