The solubility of the alkaline earth's metal sulphates in water decreases in the sequence:

The lattice energies of alkaline earth sulphates are almost constant, but $\mathrm{Hydration} energy\propto \frac{1}{\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{ }\mathrm{o}\mathrm{f} \mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}$

For $\mathrm{M}{\mathrm{g}}^{2+}\to \mathrm{C}{\mathrm{a}}^{2+}\to \mathrm{S}{\mathrm{r}}^{2+}\to \mathrm{B}{\mathrm{a}}^{2+}$ , the cationic size increases, so the hydration energy decreases, i.e. $\mathrm{M}\mathrm{g}\mathrm{S}{\mathrm{O}}_4$ is soluble and $\mathrm{B}\mathrm{a}\mathrm{S}{\mathrm{O}}_4$ is a precipitate.

$\mathrm{M}\mathrm{g}\mathrm{S}{\mathrm{O}}_4>\mathrm{C}\mathrm{a}\mathrm{S}{\mathrm{O}}_4>\mathrm{S}\mathrm{r}\mathrm{S}{\mathrm{O}}_4>\mathrm{B}\mathrm{a}\mathrm{S}{\mathrm{O}}_4$