Formally, we can prove by Induction , but let me give you an intuitive idea.
There are two types of derivations , one which is of the form A$\rightarrow$TD and A$\rightarrow$b.
To generate a string of length we need n-1 derivations of the form A$\rightarrow$TD. And to finally replace the non-terminals , we need n productions of the form A$\rightarrow$b to replace each non-terminal to a terminal.
Hence, we need n-1+n=2n-1 productions in all exactly , to get a string of length n.