1. **Problem Statement:** Find the general term, the 10th term, and the first three terms of an arithmetic progression (A.P.) where the first term $a_1=4$ and the common difference $d=-5$. 2. **Formula for the general term of an A.P.:** $$a_n = a_1 + (n-1)d$$ where $a_n$ is the $n^{th}$ term, $a_1$ is the first term, and $d$ is the common difference. 3. **Calculate the general term:** Substitute $a_1=4$ and $d=-5$ into the formula: $$a_n = 4 + (n-1)(-5) = 4 - 5(n-1) = 4 - 5n + 5 = 9 - 5n$$ 4. **Find the 10th term:** Substitute $n=10$ into the general term: $$a_{10} = 9 - 5(10) = 9 - 50 = -41$$ 5. **Find the first three terms:** - For $n=1$: $$a_1 = 9 - 5(1) = 9 - 5 = 4$$ - For $n=2$: $$a_2 = 9 - 5(2) = 9 - 10 = -1$$ - For $n=3$: $$a_3 = 9 - 5(3) = 9 - 15 = -6$$ **Final answers:** - General term: $$a_n = 9 - 5n$$ - 10th term: $$a_{10} = -41$$ - First three terms: $$4, -1, -6$$