1. **State the problem:** Find the sum to infinity of the geometric progression (GP) 48, 12, 3, 0.75, ... 2. **Identify the first term and common ratio:** The first term $a = 48$. 3. To find the common ratio $r$, divide the second term by the first term: $$r = \frac{12}{48} = \frac{1}{4}$$ 4. **Check if the sum to infinity exists:** The sum to infinity of a GP exists only if $|r| < 1$. Here, $|\frac{1}{4}| = 0.25 < 1$, so the sum exists. 5. **Formula for sum to infinity:** $$S_\infty = \frac{a}{1 - r}$$ 6. **Substitute values:** $$S_\infty = \frac{48}{1 - \frac{1}{4}} = \frac{48}{\frac{3}{4}}$$ 7. Simplify the denominator: $$S_\infty = 48 \times \frac{4}{3}$$ 8. Calculate the product: $$S_\infty = 64$$ **Final answer:** The sum to infinity of the GP is $64$.