1. **Problem statement:** Find the value of the sequence terms $U_0$ to $U_4$ given $U_0=0$ and $U_1=\sqrt{U_0 + 12}$. 2. **Formula and rules:** The sequence is defined recursively with initial values. We calculate each term step-by-step. 3. **Calculate $U_1$:** $$U_1 = \sqrt{U_0 + 12} = \sqrt{0 + 12} = \sqrt{12} = 2\sqrt{3}$$ 4. **Calculate $U_2$:** Assuming the same rule applies, $U_2 = \sqrt{U_1 + 12}$ $$U_2 = \sqrt{2\sqrt{3} + 12}$$ 5. **Calculate $U_3$:** $$U_3 = \sqrt{U_2 + 12} = \sqrt{\sqrt{2\sqrt{3} + 12} + 12}$$ 6. **Calculate $U_4$:** $$U_4 = \sqrt{U_3 + 12} = \sqrt{\sqrt{\sqrt{2\sqrt{3} + 12} + 12} + 12}$$ 7. **Summary:** The terms are: - $U_0 = 0$ - $U_1 = 2\sqrt{3}$ - $U_2 = \sqrt{2\sqrt{3} + 12}$ - $U_3 = \sqrt{\sqrt{2\sqrt{3} + 12} + 12}$ - $U_4 = \sqrt{\sqrt{\sqrt{2\sqrt{3} + 12} + 12} + 12}$ These are exact forms; numerical approximations can be computed if needed. **Note:** The limits given are not solved here as per instructions to solve only the first problem.