PV=nRT..... Kinetic theory of gases problem.................

Initial pressure = P   Volume = V       Let the initial temperature be T
     P V = n R T

stroke volume of the pump = v  (let v

Assuming an isothermal process:
    After the pumping out gas of volume v out of  V, the number of moles of the given gas left in the container = n *(V-v)/V
    As Volume V of the container is constant, 
    P1 = P * (V-v)/V = P (1 - v/V)

Again when gas is pumped out pressure will become
    P2 = P1 * (1 - v/V) = P (1- v/V)²

After n pumpings,  Pressure inside the container = P (1 - v/V)ⁿ