if $H^{n+1}(G,A)=0$ for all $G$-module $A$ ,then $H^{k}(G,A)=0$ for all $k>n$ and for all $G$-modules $A$.

Question

if $H^{n+1}(G,A)=0$ for all $G$-module $A$ ,then $H^{k}(G,A)=0$ for all $k>n$ and for all $G$-modules $A$.

any hint or idea or references to study will be great,thanks.