Proof that the rth term can be found by finding the difference between the sum of the first r terms and the sum of the first (r-1) terms: That is, $\displaystyle U_{r} = S_{r}-S_{r-1}$.

What I really don't understand is $\displaystyle S_{r-1}$. For example, what is the $\displaystyle S_{r-1}$ of $\displaystyle 3+5+7+9$? Is it $\displaystyle 0+3+5+7$? Or $\displaystyle 1+3+5+7$?