In a geometric sequence, the 3rd term is 18 and the 5th term is 162. Given that the common ratio is positive, find the first term of the sequence.
Answer & Analysis
Analysis
Question Analysis
This question evaluates the student's ability to find the first term of a geometric sequence given two non-adjacent terms and the condition that the common ratio is positive.
Key Concept Explanation
The common ratio can be found by dividing the 5th term by the 3rd term and then taking the square root. Once the common ratio is known, the first term can be calculated using the 3rd term and the common ratio.
Step-by-step Solution
1. Set up the ratio:
2. Since the difference in positions is 2, take the square root:
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