A common reason given on why 3rd ionization energy > 2nd > 1st is because of increasing effective nuclear charge.
As per my book $Z_\mathrm{eff}$ = Atomic number $-$ Number of inner electrons.
Now let us consider a Carbon atom. C has an Electronic configuration of $\ce{[He] 2s^2 2p^2}$ or $2,4$
Right now the effective nuclear charge is $6 - 2 = 4$
Now if we remove the first electron the first ionization energy will be $=\pu{1086.45 kJ/mol}$
After doing this effective nuclear chrarge is still $6 - 2 = 4$
Now if we remove the second electron the second ionization energy will be $=\pu{2352.62 kJ/mol}$
If the effective nuclear charge in removal of 1st and 2nd electron is same then why is 2nd ionization energy > 1st.
note : these values are taken from here