Firstly, we must consider the definition of first ionisation energy (1st IE). Thermodynamically, it is the enthalpy change when one mole of electrons is removed from a mole of gaseous atoms of a particular element to form a mole of singly charged gaseous ions:
A (g) → A+ (g) + e-
Next, we must think about what changes physically as we move down a group in the periodic table and how this will affect this enthalpy change. We know that moving one step down a group means the addition of a number of protons to the nucleus, increasing nuclear charge. However, we also know it involves the addition of an extra complete shell of electrons between the nucleus and the outer electron, increasing atomic radius. This shell will have a shielding effect on the electrostatic attraction between the outer electron and the nucleus, outweighing the attraction due to the additional protons. Therefore, the attraction between nucleus and outer electron is weaker moving down the group, so less energy is required to remove it, resulting in a lowering in 1st IE. This means a negative trend is expected.