1. The problem is to find the $r$-th term ($U_r$) of the sequence: 4, 8, 16, ... 2. Identify the type of sequence. The terms are 4, 8, 16, which increase by multiplication, so this is a geometric sequence. 3. Find the first term $a$ and common ratio $r$. Here, $a = 4$ and the ratio $r = \frac{8}{4} = 2$. 4. The formula for the $r$-th term of a geometric sequence is: $$ U_r = a \times r^{r-1} $$ 5. Substitute the values: $$ U_r = 4 \times 2^{r-1} $$ 6. This formula gives the $r$-th term of the sequence. Final answer: $$ U_r = 4 \times 2^{r-1} $$