1. **State the problem:** We have a sequence defined by the recurrence relation $$u_{n+1} = k u_n + k$$ where $k$ is a constant. Given: $$u_1 = 9$$ and $$u_2 = 4$$. We need to find the value of $$u_4$$. 2. **Use the recurrence relation:** From the definition, $$u_2 = k u_1 + k$$ Substitute the known values: $$4 = k \times 9 + k = 9k + k = 10k$$ 3. **Solve for $k$:** $$4 = 10k$$ $$\Rightarrow k = \frac{4}{10} = \frac{2}{5}$$ 4. **Find $u_3$ using the recurrence:** $$u_3 = k u_2 + k = \frac{2}{5} \times 4 + \frac{2}{5} = \frac{8}{5} + \frac{2}{5} = \frac{10}{5} = 2$$ 5. **Find $u_4$ using the recurrence:** $$u_4 = k u_3 + k = \frac{2}{5} \times 2 + \frac{2}{5} = \frac{4}{5} + \frac{2}{5} = \frac{6}{5} = 1.2$$ **Final answer:** $$u_4 = 1.2$$