What is the relationship between atmospheric pressure and the density of gas particles in an area of increasing pressure?

At atmospheric pressure, a gas will have a certain density at that pressure. Density is measured a mass divided by the volume. If you increase the pressure in a cylinder of constant mass of gas particles, you decrease the volume at which gases occupy thus from the equation density is equal to mass over volume, a volume decrease with a constant mass yields a higher density. Therefore increasing the pressure increases the density.