In a geometric sequence, the 2nd term is 10 and the 4th term is 40. Find the common ratio and the first term .
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to find the first term and the common ratio 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 .
3. Divide the second equation by the first:
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