Let $\{T_n\}$ be a sequence of mappings from metric space $(X,d)$ into itself which converges pointwise to the contraction mapping $T$. $T^{n+1}=T_{n+1}T^n$ is identified with $T_1=T^1$ and the convergence of the sequence $\{T^nx\}$ is investigated for any point $x\in X$.