2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142478In this paper we shall consider the growth at infinity of a sequence $(P_n)$ of entire functions of bounded orders. Our results extend the results in \cite{trong-tuyen2} for the growth of entire functions of genus zero. Given a sequence of entire functions of bounded orders $P_n(z)$, we found a nearly optimal condition, given in terms of zeros of $P_n$, for which $(k_n)$ that we have \begin{eqnarray*} \limsup_{n\to\infty}|P_n(z)|^{1/k_n}\leq 1 \end{eqnarray*} for all $z\in \mathbb C$ (see Theorem \ref{theo5}). Exploring the growth of a sequence of entire functions of bounded orders lead naturally to an extremal function which is similar to the Siciak's extremal function (See Section 6).19 pages. Some typos are correctedComplex Variables30C85, 30D15, 31A15text