A geometric sequence has a 3rd term and a common ratio . Find the 6th term, .
Answer & Analysis
Analysis
Question Analysis
The question requires students to find the 6th term of a geometric sequence given the 3rd term and the common ratio. Students need to first find the first term and then use the explicit formula to find the 6th term.
Key Concept Explanation
The explicit formula for the nth term of a geometric sequence is (). To find the 6th term, students must first determine the first term using the 3rd term and the common ratio.
Step-by-step Solution
1. Identify the given values: , , and .
2. Use the 3rd term to find the first term: .
3. Solve for :
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