  We have considered that the universe is the inhomogeneous $(n+2)$ dimensional
quasi-spherical Szekeres space-time model. We consider the universe as a
thermodynamical system with the horizon surface as a boundary of the system. To
study the generalized second law (GSL) of thermodynamics through the universe,
we have assumed the trapped surface is the apparent horizon. Next we have
examined the validity of the generalized second law of thermodynamics (GSL) on
the apparent horizon by two approaches: (i) using first law of thermodynamics
on the apparent horizon and (ii) without using the first law. In the first
approach, the horizon entropy have been calculated by the first law. In the
second approach, first we have calculated the surface gravity and temperature
on the apparent horizon and then horizon entropy have found from area formula.
The variation of internal entropy have been found by Gibb's law. Using these
two approaches separately, we find the conditions for validity of GSL in
$(n+2)$ dimensional quasi-spherical Szekeres model.
