New Solutions for Evolution of the Scale Factor with a Variable Cosmological Term

The cosmological term is assumed to be a function of time such as $\Lambda =Ba^{-2}$ where a(t) means the scale factor of standard cosmology. Analytical solutions for radiation dominated epoch and open universe are found. For closed universe, k=+1, and for flat universe, k=0, we show a numerical solution. In general the scenario of Big Bang is preserved in our case for the Friedmann-Robertson-Walker cosmology.