In a geometric sequence, the 5th term is 128 and the 7th term is 512. Find the common ratio and the first term .
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to find the common ratio and the first term of a geometric sequence given two non-adjacent 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. Given: and .
2. Using the explicit formula: and
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