The $+1$ oxidation state in group $13$ and $+2$ oxidation state in group $14$ become more stable with increasing atomic number. Explain.

(N/A) On moving down the group in group $13$ and $14$,the lower oxidation state becomes more stable compared to the higher oxidation state due to the $\text{inert pair effect}$.
In the $\text{inert pair effect}$,the $ns^2$ electrons of the valence shell do not participate in bonding,and only $np$ electrons participate. As the size of the atom increases,the energy required to unpair the $ns^2$ electrons becomes significantly higher than the energy released during bond formation.
In group $13$,the valence shell configuration is $ns^2 np^1$. When both $s$ and $p$ electrons participate,they show a $+3$ oxidation state,but if only $p$ electrons participate,they show a $+1$ oxidation state.
In group $14$,the valence shell configuration is $ns^2 np^2$. When both $s$ and $p$ electrons participate,they show a $+4$ oxidation state,but if only $p$ electrons participate,they show a $+2$ oxidation state.