1. The problem is to find the general term formula $x_n$ for the sequence: 5, $\frac{5}{2}$, $\frac{5}{4}$, ... 2. This is a geometric sequence where each term is obtained by multiplying the previous term by a common ratio $r$. 3. To find $r$, divide the second term by the first term: $$r = \frac{\frac{5}{2}}{5} = \frac{5}{2} \times \frac{1}{5} = \frac{1}{2}$$ 4. The first term $a_1$ is 5. 5. The general formula for the $n$-th term of a geometric sequence is: $$x_n = a_1 \times r^{n-1}$$ 6. Substitute $a_1 = 5$ and $r = \frac{1}{2}$: $$x_n = 5 \times \left(\frac{1}{2}\right)^{n-1}$$ 7. This matches options C and E, which are the same formula. Final answer: $$x_n = 5 \times \left(\frac{1}{2}\right)^{n-1}$$