  As an alternative to dark energy that explains the observed acceleration of
the universe, it has been suggested that we may be at the center of an
inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB)
solution of Einstein's field equations. To test this possibility, it is
necessary to solve the null geodesics. In this paper we first give a detailed
derivation of a fully analytical set of differential equations for the radial
null geodesics as functions of the redshift in LTB models. As an application we
use these equaions to show that a positive averaged acceleration $a_D$ obtained
in LTB models through spatial averaging can be incompatible with cosmological
observations. We provide examples of LTB models with positive $a_D$ which fail
to reproduce the observed luminosity distance $D_L(z)$. Since the apparent
cosmic acceleration $a^{FLRW}$ is obtained from fitting the observed luminosity
distance to a FLRW model we conclude that in general a positive $a_D$ in LTB
models does not imply a positive $a^{FLRW}$.
