In a geometric sequence, the 3rd term is and the 5th 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 3rd and 5th 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 3rd term:
2. Use the explicit formula for the 5th term:
3. Divide the second equation by the first:
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