Consider a geometric sequence where the first term is 10 and the common ratio is . Find the 6th term of the sequence. The 6th term is _______.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to use the explicit formula for a geometric sequence with a fractional common ratio to find a specific term.
Key Concept Explanation
The explicit formula for the -th term of a geometric sequence is given by (), where is the first term, is the common ratio, and is the term number.
Step-by-step Solution
1. Identify the first term and the common ratio .
2. Use the explicit formula to find the 6th term.
3. Substitute
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