1. **State the problem:** We are given the sum of a series from $n=3$ to $n=18$ of the terms defined by $6n - 10$. We need to find the first term ($a_1$), the last term ($a_{last}$), and the sum of the series.
2. **Identify the terms:** The general term is $a_n = 6n - 10$.
3. **Find the first term:** Since the series starts at $n=3$, the first term is
$$a_3 = 6(3) - 10 = 18 - 10 = 8.$$
4. **Find the last term:** The last term corresponds to $n=18$, so
$$a_{18} = 6(18) - 10 = 108 - 10 = 98.$$
5. **Number of terms:** The number of terms from $n=3$ to $n=18$ is
$$18 - 3 + 1 = 16.$$
6. **Sum of the series:** The sum of an arithmetic series is given by
$$S = \frac{n}{2}(a_1 + a_n),$$
where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term.
7. Substitute the values:
$$S = \frac{16}{2}(8 + 98) = 8 \times 106 = 848.$$
**Final answers:**
- First term $a_1 = 8$
- Last term $a_{last} = 98$
- Sum $S = 848$
Arithmetic Series 77Cdd4
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