1. The problem is to find the explicit formula for the geometric sequence given: 12, 6, 3, 1.5, 0.75, ... 2. The general formula for a geometric sequence is: $$f(n) = a \cdot r^{n-1}$$ where $a$ is the first term and $r$ is the common ratio. 3. Identify the first term $a$ from the sequence: The first term $a = 12$. 4. Find the common ratio $r$ by dividing the second term by the first term: $$r = \frac{6}{12} = \frac{1}{2}$$ 5. Substitute $a = 12$ and $r = \frac{1}{2}$ into the formula: $$f(n) = 12 \cdot \left(\frac{1}{2}\right)^{n-1}$$ 6. This formula generates the sequence by multiplying the previous term by $\frac{1}{2}$ each time. Final answer: $$f(n) = 12 \cdot \left(\frac{1}{2}\right)^{n-1}$$