In a geometric sequence, the 2nd term is and the 4th term is . Find the first term .
Answer & Analysis
Analysis
Question Analysis
This question requires students to find the first term of a geometric sequence given two non-adjacent terms, the 2nd and 4th terms.
Key Concept Explanation
The key concept here is using the explicit formula for geometric sequences, (), and setting up equations to solve for and .
Step-by-step Solution
1. Use the explicit formula for the 2nd term:
2. Use the explicit formula for the 4th term:
3. Divide the second equation by the first:
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