Let $G$ be group and let $M$ be a $G$-module. The module $M$ is said to be of type $FP_n$ if there exists an exact seqeunce $$ P_n \rightarrow P_{n-1} \rightarrow \ldots \rightarrow P_1 \rightarrow P_0 \rightarrow M \rightarrow 0$$ where all the $P_i$ are finitely generated projective $G$-modules.
It is known that a $G$-module $M$ is of type $FP_n$ iff for every exact colimit, the natural map $$\mathrm{colim}\ \mathrm{Ext}^k_{\mathbb{Z}[G]}(M,N_{\ast}) \rightarrow \mathrm{Ext}^k_{\mathbb{Z}[G]}(M,\mathrm{colim}\ N_{\ast})$$ is an isomorphims for $k<n$ and a monomorphism for k=n.
Using this result one can show that a direct summand of a module of type $FP_n$ is also of type $FP_n$. My question is: is there a more explicit proof of this fact, which does not use the result mentioned above?