Condition for an entire function to be a polynomial

Question

I need a hint to solve the following problem.

Shows that if $f:\mathbb{C}\rightarrow\mathbb{C}$ is an entire function that satisfies $\lim_{n\rightarrow\infty}|f(z_n)|=\infty$ provided that a sequence $(z_n)_{n=1}^\infty$ satisfies $lim_{n\rightarrow\infty}z_n=\infty$, then $f$ is a polynomial.