# Reproducing Gauss' famous proof

The following appears in a text (in the context of generalizing Gauss' famous proof):

I would like to reproduce this, but I cannot figure out how to get the alignment down. I thought of trying to use alignat but that does not seem to help (or maybe I simply do not know how to use it properly). Also, I would like for the horizontal line to be placed properly, but this is what I have come up with so far which is rather poor:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{align*}
S_n &=& a &+& (a+d) &+\cdots+& [a+(n-1)d]\\
S_n &=& [a+(n-1)d] &+& [a+(n-2)d] &+\cdots+& a\\\hline
2S_n &=& [2a+(n-1)d]&+& [2a+(n-1)d &+\cdots+&[2a+(n-1)d]
\end{align*}

\end{document}


which gives

Any ideas on how to obtain the first image effectively?

You're better using an array (with some tricks):

\documentclass{article}
\usepackage{amsmath,booktabs,array}

\begin{document}

\begin{equation*}
\setlength{\arraycolsep}{0pt}
\begin{array}{ r *{5}{ >{{}}c<{{}} c } }
S_n &=& a           &+& (a+d)      &+& \cdots &+& [a+(n-1)d]\\

The >{{}}c<{{}} columns ensure correct spacing around the equals and plus signs, together with \arraycolsep set to zero.