1. The formulas for the sum of arithmetic series are typically denoted as $S_1 = \frac{n}{2}(a_1 + a_n)$ or $S_2 = \frac{n}{2}(2a_1 + (n-1)d)$. 2. Here, $n$ is the number of terms, $a_1$ is the first term, $a_n$ is the last term, and $d$ is the common difference. 3. $S_1$ is used when you know the first and last terms of the series. 4. $S_2$ is used when you know the first term, the number of terms, and the common difference, but not the last term. 5. To select the appropriate formula, check which values you have: - If you have the last term $a_n$, use $S_1$. - If you do not have $a_n$ but have $d$, use $S_2$. 6. Using the correct formula ensures correctly calculating the sum of the arithmetic series.