In a geometric sequence, the 4th term is and the 6th term is . Find the first term . The first term is _______.
Answer & Analysis
Analysis
Question Analysis
This question requires students to find the first term of a geometric sequence given two non-adjacent terms, the 4th and 6th 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 4th term:
2. Use the explicit formula for the 6th term:
3. Divide the second equation by the first:
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