  Implications of cosmological model with a cosmological term of the form
$\Lambda = \beta \frac{\ddot {a}}{a}$, where $\beta$ is a constant, are
analyzed in multidimensional space time. The proper distance, the luminosity
distance-redshift, the angular diameter distance-redshift, and look back
time-redshift for the model are presented. It has been shown that such models
are found to be compatible with the recent observations. This work has thus
generalized to higher dimensions the well-know result in four dimensional space
time. It is found that there may be significant difference in principle at
least,from the analogous situation in four dimensional space time.
