1. **Problem:** Find which term 2048 is in the geometric sequence 2, 8, 32, 128, ... 2. **Formula:** The $n$th term of a geometric sequence is given by $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 3. **Identify values:** Here, $a_1 = 2$ and $r = \frac{8}{2} = 4$. 4. **Set up equation:** We want to find $n$ such that $$a_n = 2048 = 2 \times 4^{n-1}$$ 5. **Solve for $n$:** Divide both sides by 2: $$4^{n-1} = \frac{2048}{2} = 1024$$ 6. Recognize that $1024 = 4^5$ because $4^5 = (2^2)^5 = 2^{10} = 1024$. 7. Therefore, $$4^{n-1} = 4^5 \implies n-1 = 5 \implies n = 6$$ **Final answer:** 2048 is the 6th term of the sequence.