Although +3 oxidation stae is thje characteristic oxidation state of lanthanoids but cerium shows +4 oxidation state also. Why ?

Explanation

Cerium `(Z=58)` has electronic configuration `[Xe]4f^(1)5d^(1)6s^(2)`. By losing three electrons, `Ce^(3+)` ion has the configuration `[Xe]4f^(1)`. It has quite obviously an urge to get rid of `4f^(1)` electron as well to achieve a noble gas configuration. Therefore, it also shows `+4` oxidation state in its compounds.