1. **State the problem:** We are given the first term $a_1 = -20$ of an arithmetic sequence and the fourth term $a_4 = -2$. We need to find the eighth term $a_8$. 2. **Recall the formula for the $n$th term of an arithmetic sequence:** $$a_n = a_1 + (n-1)d$$ where $d$ is the common difference. 3. **Find the common difference $d$ using the fourth term:** $$a_4 = a_1 + 3d$$ Substitute the known values: $$-2 = -20 + 3d$$ 4. **Solve for $d$:** $$-2 + 20 = 3d$$ $$18 = 3d$$ $$d = \frac{18}{3}$$ $$d = 6$$ 5. **Find the eighth term $a_8$ using the formula:** $$a_8 = a_1 + 7d$$ Substitute $a_1 = -20$ and $d = 6$: $$a_8 = -20 + 7 \times 6$$ $$a_8 = -20 + 42$$ $$a_8 = 22$$ **Final answer:** The eighth term of the arithmetic sequence is $22$.