1. The problem is to find the formula to determine the number of terms in an arithmetic series. 2. An arithmetic series is the sum of terms in an arithmetic sequence, where each term increases by a constant difference $d$. 3. The $n$th term of an arithmetic sequence is given by the formula: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term, $d$ is the common difference, and $n$ is the number of terms. 4. To find the number of terms $n$ when you know the first term $a_1$, the last term $a_n$, and the common difference $d$, rearrange the formula: $$a_n = a_1 + (n-1)d$$ $$a_n - a_1 = (n-1)d$$ $$\frac{a_n - a_1}{d} = n - 1$$ $$n = \frac{a_n - a_1}{d} + 1$$ 5. This formula tells you how many terms are in the arithmetic sequence given the first term, last term, and common difference. 6. Important rules: - The common difference $d$ cannot be zero. - The terms must form an arithmetic sequence. 7. Summary: To find the number of terms $n$ in an arithmetic series, use the formula: $$n = \frac{a_n - a_1}{d} + 1$$