A geometric sequence has the first term 100 and a common ratio of . Write the explicit formula for the n-th term of this sequence. Using this formula, find the 6th term. The 6th term is _______.
Answer & Analysis
Analysis
Question Analysis
This question evaluates the student's ability to write the explicit formula for a geometric sequence and use it to find a specific term, particularly when the common ratio is a fraction.
Key Concept Explanation
The explicit formula for the -th term of a geometric sequence is (), where is the first term and is the common ratio.
Step-by-step Solution
1. Identify the first term and the common ratio .
2. Write the explicit formula:
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