1. The problem is about numerical processes related to sequences and series. 2. Let's begin by understanding what a sequence is: a list of numbers arranged in a specific order. 3. A series is the sum of the terms of a sequence. 4. For example, consider the arithmetic sequence with first term $a_1$ and common difference $d$. 5. The $n$th term is given by $a_n = a_1 + (n-1)d$. 6. The sum of the first $n$ terms of an arithmetic series is given by $$S_n = \frac{n}{2} (2a_1 + (n-1)d).$$ 7. For geometric sequences with first term $a_1$ and common ratio $r$, the $n$th term is $a_n = a_1 r^{n-1}$. 8. The sum of the first $n$ terms of a geometric series is $$S_n = a_1 \frac{1-r^n}{1-r}$$ for $r\neq1$. 9. We can use these formulas to solve numerical process problems for sequences and series.