\begin{equation*} \begin{aligned} a_1 - a_0 \amp = 2^1\\ a_2 - a_1 \amp = 2^2\\ a_3 - a_2 \amp = 2^3\\ \vdots\amp \vdots\\ a_n - a_{n-1} \amp = 2^n \end{aligned} \end{equation*}