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

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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} = 1left(-frac{1}{2}right)^{n-1} )

Answer

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} = 1left(-frac{1}{2}right)^{n-1} )

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

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