Example 2.1.5.
Sam keeps track of how many push-ups she does each day of her “do lots of push-ups challenge.” Let \((a_n)_{n \ge 1}\) be the sequence that describes the number of push-ups done on the \(n\)th day of the challenge. The sequence starts
\begin{equation*}
3, 5, 6, 10, 9, 0, 12, \ldots\text{.}
\end{equation*}
Describe a sequence \((b_n)_{n \ge 1}\) that describes the total number of push-ups done by Sam after the \(n\)th day.