1. The problem involves finding the first term $a_1$ and the general term $a_n$ of an arithmetic sequence given a specific term $a_{13} = 15$ and common difference $d = 4$. 2. The formula for the $n$-th term of an arithmetic sequence is: $$a_n = a_1 + (n-1)d$$ 3. Substitute $n=13$, $a_{13} = 15$, and $d=4$ into the formula: $$15 = a_1 + (13-1) \times 4$$ $$15 = a_1 + 12 \times 4$$ $$15 = a_1 + 48$$ 4. Solve for $a_1$: $$a_1 = 15 - 48$$ $$a_1 = -33$$ 5. Now write the general term $a_n$ using $a_1 = -33$ and $d=4$: $$a_n = -33 + (n-1) \times 4$$ $$a_n = -33 + 4n - 4$$ $$a_n = 4n - 37$$ Final answers: - First term: $a_1 = -33$ - General term: $a_n = 4n - 37$