When we think about how the first and last numbers in a set of numbers affect the total, it's pretty interesting. Let's break it down step by step:

1. What is an Arithmetic Series?
   An arithmetic series is a group of numbers where each number is the same distance away from the one before it. This means that the first number (let’s call it $a_1$) and the last number ($a_n$) are super important for figuring out the total sum.

2. How to Find the Total Sum:
   We can use a simple formula to find the total of an arithmetic series:
   $S_n = \frac{n}{2} \cdot (a_1 + a_n)$
   In this formula, $n$ is how many numbers are in the series.

3. How $a_1$ and $a_n$ Matter:

   • If you change $a_1$ (the first number), it impacts the whole total. For instance, if you start with a bigger $a_1$, the total sum will also be bigger.
   • The same thing happens with the last number, $a_n$. If $a_n$ goes up, the total sum goes up too.

To sum it all up, changing the first or last number in an arithmetic series changes the total sum. That’s why it’s important to pay attention to these first and last numbers when looking at these kinds of series!