The species $Ca^{2+}$, $K^+$, $Ar$, $Cl^-$, and $S^{2-}$ are isoelectronic, meaning they all possess the same number of electrons (18 electrons). For isoelectronic species, the ionic radius decreases as the nuclear charge (atomic number, Z) increases.

The atomic numbers are: $S$ (Z = 16) $Cl$ (Z = 17) $Ar$ (Z = 18) $K$ (Z = 19)

• $Ca$ (Z = 20)

A higher nuclear charge pulls the same number of electrons more strongly towards the nucleus, resulting in a smaller size. Therefore, the size decreases in the order of increasing atomic number: $S^{2-} > Cl^- > Ar > K^+ > Ca^{2+}$. Conversely, the increasing order of size is $Ca^{2+} < K^+ < Ar < Cl^- < S^{2-}$.