In a geometric sequence, the 3rd term is 12 and the 5th term is 48. Find the first term . ()
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to find the first term of a geometric sequence given two non-adjacent terms.
Key Concept Explanation
The common ratio can be found by setting up a ratio between the 5th term and the 3rd term, then solving for . Once is known, the first term can be calculated using the relationship between the 3rd term and .
Step-by-step Solution
1. Set up the ratio:
2. Express the ratio in terms of :
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