To find the common ratio of the given sequence, we should observe how the y-values change as the x-values increase. You've provided the points in the sequence as follows:
- \( (0, 3) \)
- \( (1, 3.6) \)
- \( (2, 4.32) \)
- \( (3, 5.184) \)
Let's denote the y-values of these points as \( y_0 = 3 \), \( y_1 = 3.6 \), \( y_2 = 4.32 \), and \( y_3 = 5.184 \).
We will calculate the ratio of each subsequent term to the previous term:
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From \( y_0 \) to \( y_1 \): \[ r_1 = \frac{y_1}{y_0} = \frac{3.6}{3} = 1.2 \]
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From \( y_1 \) to \( y_2 \): \[ r_2 = \frac{y_2}{y_1} = \frac{4.32}{3.6} = 1.2 \]
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From \( y_2 \) to \( y_3 \): \[ r_3 = \frac{y_3}{y_2} = \frac{5.184}{4.32} = 1.2 \]
Since the ratio \( r \) is consistent throughout the sequence, the common ratio of the series is:
\[ \text{Common Ratio} = 1.2 \]