Question

What is the common ratio of this sequence? (1 point)

Graph starting point-(0,3)
Second point-(1,3.6)
third point-(2,4.32)
fourth point-(3,5.184)

Answer 1

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:

1. \( (0, 3) \)
2. \( (1, 3.6) \)
3. \( (2, 4.32) \)
4. \( (3, 5.184) \)

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:

1. From \( y_0 \) to \( y_1 \):
\[
r_1 = \frac{y_1}{y_0} = \frac{3.6}{3} = 1.2
\]

2. From \( y_1 \) to \( y_2 \):
\[
r_2 = \frac{y_2}{y_1} = \frac{4.32}{3.6} = 1.2
\]

3. 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:

\[
\text{Common Ratio} = 1.2
\]