If \( a_{n}=\frac{1}{1024} \) for the geometric sequence \( 1,-\frac{1}{2}, \frac{1}{4}, \ldots \), find \( n \).

Step 1 ：1. Identify the common ratio: \( r = -\frac{1}{2} \)

Step 2 ：2. Apply the geometric sequence formula: \( a_{n} = a_{1}r^{n-1} \)

Step 3 ：3. Solve for \( n \): \( \frac{1}{1024} = 1\left(-\frac{1}{2}\right)^{n-1} \)