1. **State the problem:** We are given a recursive arithmetic sequence defined by $a_n = a_{n-1} + 7$ with the first term $a_1 = -5$. We need to find the values of $a_4$ and also analyze the function $f(n) = f(n-1) - 8$ with $f(1) = 10$. 2. **Formula for arithmetic sequences:** The general term of an arithmetic sequence is given by: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. 3. **Identify values:** Here, $a_1 = -5$ and $d = 7$. 4. **Calculate $a_4$:** $$a_4 = a_1 + (4-1) \times 7 = -5 + 3 \times 7 = -5 + 21 = 16$$ 5. **Analyze $f(n)$:** The function $f(n) = f(n-1) - 8$ with $f(1) = 10$ is also a recursive arithmetic sequence with common difference $-8$. 6. **General formula for $f(n)$:** $$f(n) = f(1) + (n-1)(-8) = 10 - 8(n-1)$$ 7. **Calculate $f(4)$:** $$f(4) = 10 - 8(4-1) = 10 - 8 \times 3 = 10 - 24 = -14$$ **Final answers:** - $a_4 = 16$ - $f(4) = -14$