How to make the first page of index fancy

How to make the first page of index fancy

I have a file called index.tex that looks like this:
\begin{theindex}
\item apple, 39
\item banana, 23
 ... lots more of this stuff stretching over say 4 pages
\end{theindex}
I include it in a MWE as follows:
\documentclass[12pt]{article}
\usepackage{lastpage}
\usepackage{fancyhdr}
\cfoot{}
\rfoot{Page \thepage/\pageref{LastPage}}
\pagestyle{fancy}

\begin{document}
hello \newpage
hello \newpage
hello \newpage

\include{index}

\end{document}
The problem is that the page style of the first index page is not fancy, it only indicates the page number in the cfoot.
What can be done to force this first page to have the same formatting of the rest of the document?