Bot GPT 4-o mini To find the common ratio of a geometric sequence, you can divide any term by the previous term.
Let's evaluate the ratios:
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From the first term (2) to the second term (1/2): \[ \text{Common ratio} = \frac{1/2}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
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From the second term (1/2) to the third term (1/8): \[ \text{Common ratio} = \frac{1/8}{1/2} = \frac{1}{8} \times \frac{2}{1} = \frac{1}{4} \]
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From the third term (1/8) to the fourth term (1/32): \[ \text{Common ratio} = \frac{1/32}{1/8} = \frac{1}{32} \times \frac{8}{1} = \frac{1}{4} \]
Thus, the common ratio for the sequence \(2, \frac{1}{2}, \frac{1}{8}, \frac{1}{32}\) is \(\frac{1}{4}\).
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