1. **Statement of the problem:** Calculate the first three terms of the sequence $(u_n)$ defined by: $$u_n = -3n + 2$$ and also for the sequence defined by the recurrence: $$u_0 = 2$$ $$u_{n+1} = 3u_n - 1$$ 2. **First sequence $(u_n = -3n + 2)$:** - For $n=0$: $$u_0 = -3 \times 0 + 2 = 2$$ - For $n=1$: $$u_1 = -3 \times 1 + 2 = -3 + 2 = -1$$ - For $n=2$: $$u_2 = -3 \times 2 + 2 = -6 + 2 = -4$$ 3. **Second sequence defined by recurrence:** - Given initial term: $$u_0 = 2$$ - Calculate $u_1$: $$u_1 = 3u_0 - 1 = 3 \times 2 - 1 = 6 - 1 = 5$$ - Calculate $u_2$: $$u_2 = 3u_1 - 1 = 3 \times 5 - 1 = 15 - 1 = 14$$ **Final answers:** - First sequence terms: $u_0=2$, $u_1=-1$, $u_2=-4$ - Second sequence terms: $u_0=2$, $u_1=5$, $u_2=14$