A geometric sequence has its 2nd term as 5 and its 4th term as 125. Determine the first term of the sequence. The first term is ____.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to find the first term of a geometric sequence given two non-adjacent terms.
Key Concept Explanation
To find the first term of a geometric sequence, students need to use the explicit formula and solve for after finding the common ratio .
Step-by-step Solution
1. Given: and .
2. Use the explicit formula: ().
3. Set up the equations: and .
4. Divide the second equation by the first:
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