1. **State the problem:** We are given an arithmetic sequence defined by the formula $$a_n = 2 - 5(n - 1)$$ and need to find the first three terms $$a_1, a_2, a_3$$ and the common difference $$d$$. 2. **Recall the formula for an arithmetic sequence:** $$a_n = a_1 + (n-1)d$$ where $$a_1$$ is the first term and $$d$$ is the common difference. 3. **Identify the first term $$a_1$$:** Substitute $$n=1$$ into the given formula: $$a_1 = 2 - 5(1 - 1) = 2 - 5(0) = 2$$ 4. **Find the second term $$a_2$$:** Substitute $$n=2$$: $$a_2 = 2 - 5(2 - 1) = 2 - 5(1) = 2 - 5 = -3$$ 5. **Find the third term $$a_3$$:** Substitute $$n=3$$: $$a_3 = 2 - 5(3 - 1) = 2 - 5(2) = 2 - 10 = -8$$ 6. **Find the common difference $$d$$:** The common difference is the amount added each time, so: $$d = a_2 - a_1 = -3 - 2 = -5$$ **Final answers:** $$a_1 = 2$$ $$a_2 = -3$$ $$a_3 = -8$$ $$d = -5$$