The gravitational potential at a point is the scalar sum of the potentials due to individual masses. Let the point be $P$ at a distance $r = a/2$ from the centre.

1. Potential due to the particle at the centre ($V_1$): The particle behaves as a point mass. At distance $r = a/2$: $V_1 = -\frac{GM}{r} = -\frac{GM}{a/2} = -\frac{2GM}{a}$.
2. Potential due to the spherical shell ($V_2$): The point $P$ lies inside the shell ($r < a$). The gravitational potential inside a spherical shell is constant and equal to the potential at its surface. $V_2 = -\frac{GM}{R_{shell}} = -\frac{GM}{a}$.
3. Total Potential ($V$): $V = V_1 + V_2 = \left(-\frac{2GM}{a}\right) + \left(-\frac{GM}{a}\right) = -\frac{3GM}{a}$.