1. The problem gives the arithmetic sequence formula $a_n = 22 + 3(n - 1)$ and asks to find $a_1$ and $a_n$ for the sequence where $a_{13} = 15$ and $d = -7$. 2. Recall the formula for the $n$th term of an arithmetic sequence: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. 3. Given $a_{13} = 15$ and $d = -7$, substitute into the formula: $$15 = a_1 + (13-1)(-7)$$ 4. Simplify the right side: $$15 = a_1 + 12 \times (-7)$$ $$15 = a_1 - 84$$ 5. Solve for $a_1$: $$a_1 = 15 + 84 = 99$$ 6. Now write the general term $a_n$ using $a_1 = 99$ and $d = -7$: $$a_n = 99 + (n-1)(-7)$$ $$a_n = 99 - 7(n-1)$$ 7. This is the explicit formula for the arithmetic sequence with the given conditions. Final answers: $$a_1 = 99$$ $$a_n = 99 - 7(n-1)$$