A geometric sequence has a 2nd term and a common ratio . Find the 5th term. The 5th term is ______.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to use the explicit formula for the nth term of a geometric sequence when the first term is not directly given. The problem provides the 2nd term and the common ratio, and asks for the 5th term.
Key Concept Explanation
The explicit formula for the nth term of a geometric sequence is (). When the first term is not given, we need to find it using the given term and the common ratio.
Step-by-step Solution
1. Identify the given values: , .
2. Use the formula for the 2nd term to find : or .
3. Solve for :
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