1. The problem is to find an algebraic expression that represents the pattern 4, 8, 16, 32, 64, ... 2. This is a geometric sequence where each term is obtained by multiplying the previous term by a constant ratio. 3. The first term $a_1$ is 4. 4. The common ratio $r$ is found by dividing the second term by the first term: $$r = \frac{8}{4} = 2$$ 5. The general formula for the $n$-th term of a geometric sequence is: $$a_n = a_1 \times r^{n-1}$$ 6. Substitute $a_1 = 4$ and $r = 2$ into the formula: $$a_n = 4 \times 2^{n-1}$$ 7. This formula generates the sequence: for $n=1$, $a_1 = 4 \times 2^{0} = 4$; for $n=2$, $a_2 = 4 \times 2^{1} = 8$; and so on. Final answer: $$a_n = 4 \times 2^{n-1}$$