1. **Stating the problem:** We have a sequence defined by the initial term $u_0 = 6$ and the recurrence relation $u_{n+1} = 3 u_n$. We want to express $u_n$ explicitly as a function of $n$. 2. **Formula for geometric sequences:** A geometric sequence with initial term $u_0$ and common ratio $r$ is given by: $$ u_n = u_0 \times r^n $$ 3. **Identify the common ratio:** From the recurrence relation, the common ratio is $r = 3$. 4. **Write the explicit formula:** Substitute $u_0 = 6$ and $r = 3$ into the formula: $$ u_n = 6 \times 3^n $$ 5. **Explanation:** This formula means that to find the $n$-th term, multiply the initial term 6 by 3 raised to the power $n$. For example, $u_1 = 6 \times 3^1 = 18$, $u_2 = 6 \times 3^2 = 54$, and so on. **Final answer:** $$ u_n = 6 \times 3^n $$