The sequence \( u_{1}, u_{2}, u_{3}, \cdots \) is given by the recurrence relation \[ u_{n+1}=3 u_{n}+2, \quad u_{1}=2 \text {. } \] Find \( u_{2}, u_{3}, u_{4} \) and \( u_{5} \).

To find \( u_2, u_3, u_4, \) and \( u_5 \), we will use the recurrence relation \( u_{n+1} = 3u_n + 2 \) starting from the initial condition \( u_1 = 2 \). 1. **Calculate \( u_2 \)**: \[ u_2 = 3u_1 + 2 = 3 \times 2 + 2 = 6 + 2 = 8 \] 2. **Calculate \( u_3 \)**: \[ u_3 = 3u_2 + 2 = 3 \times 8 + 2 = 24 + 2 = 26 \] 3. **Calculate \( u_4 \)**: \[ u_4 = 3u_3 + 2 = 3 \times 26 + 2 = 78 + 2 = 80 \] 4. **Calculate \( u_5 \)**: \[ u_5 = 3u_4 + 2 = 3 \times 80 + 2 = 240 + 2 = 242 \] Thus, the values are: \[ u_2 = 8, \quad u_3 = 26, \quad u_4 = 80, \quad u_5 = 242. \]