In a geometric sequence, the 5th term is 48 and the 7th term is 192. Find the common ratio r of the sequence. The common ratio r is ____.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to find the common ratio of a geometric sequence given two non-adjacent terms.
Key Concept Explanation
The common ratio in a geometric sequence can be found by dividing one term by another term that is a fixed number of positions away. For non-adjacent terms, this involves solving for using the explicit formula.
Step-by-step Solution
1. Given: and .
2. Use the explicit formula: .
3. Set up the equations: and
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