A solid sphere of mass M and radius $\frac{R}{2}$ is kept concentric with a shell of equal mass and radius R.

Field due to shell, within the shell, is 0. Hence field $:\text{at }\mathrm{A}\to 0$,

$\mathrm{B}\to -\frac{\mathrm{GM}}{{\left(\frac{\mathrm{R}}{2}\right)}^2}=\frac{-4\mathrm{GM}}{{\mathrm{R}}^2}$

$\mathrm{C}\to -\frac{\mathrm{GM}}{{\mathrm{R}}^2}-\frac{\mathrm{GM}}{{\mathrm{R}}^2}=\frac{-2\mathrm{GM}}{{\mathrm{R}}^2}$

$\mathrm{D}\to -\frac{\mathrm{GM}}{4{\mathrm{R}}^2}-\frac{\mathrm{GM}}{4{\mathrm{R}}^2}=-\frac{\mathrm{GM}}{2{\mathrm{R}}^2}$

$\Rightarrow$Value as 0, 4k, 2k, $\frac{K}{2}$ neither AP or GP Potential due to shell, within the shell is constant $-\frac{\mathrm{GM}}{\mathrm{R}}$

$\therefore {\mathrm{V}}_{\mathrm{A}}=-\frac{3}{2}\frac{\mathrm{GM}}{\frac{\mathrm{R}}{2}}-\frac{\mathrm{GM}}{\mathrm{R}}=-4\frac{\mathrm{GM}}{\mathrm{R}}$

${\mathrm{V}}_{\mathrm{B}}=-\frac{\mathrm{GM}}{\frac{\mathrm{R}}{2}}-\frac{\mathrm{GM}}{\mathrm{R}}=-\frac{3\mathrm{GM}}{\mathrm{R}}$

${\mathrm{V}}_{\mathrm{C}}=-\frac{\mathrm{GM}}{\mathrm{R}}-\frac{\mathrm{GM}}{\mathrm{R}}=-2\frac{\mathrm{GM}}{\mathrm{R}}$

${\mathrm{V}}_{\mathrm{D}}=-\frac{\mathrm{GM}}{2\mathrm{R}}-\frac{\mathrm{GM}}{2\mathrm{R}}=-\frac{\mathrm{GM}}{\mathrm{R}}$

$\therefore$  Value of 4k, 3k, 2k, k in arithmetic progression.