How to prove a bound function for a sequence of numbers?
If you have tried, you will find that 
$$\begin{aligned}
G_5&amp;=6\\
G_6&amp;=7\\
G_7&amp;=8\\
G_8&amp;=9\\
G_9&amp;=10.\\
\end{aligned}$$

By now, you should have probably guessed that $G_{n}=n+1$. Now you can try proving it, using induction on $n$.

Once that formula has been proved, $f(n)=n$ is of course a lower bound for $G_n$.