Consider the sequence . Determine the common ratio of this geometric sequence. The common ratio is _________.
Answer & Analysis
Analysis
Question Analysis
This question assesses the student's ability to identify and calculate the common ratio in a geometric sequence where the terms are decreasing in magnitude. The sequence provided has a positive common ratio less than 1, which is a key characteristic of a geometric sequence that shrinks in magnitude.
Key Concept Explanation
A geometric sequence is defined by a constant ratio between consecutive terms. The common ratio can be found by dividing any term by its preceding term.
Step-by-step Solution
1. Identify the first few terms of the sequence:
2. Calculate the ratio between the second and first term:
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