Question

Which of the following correctly graphs the geometric sequence?

n f(n)
0 11
1 16.5
2 24.75
3 37.125
4 55.6875
(1 point)
Responses

[Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 6 in increments of 1 and the y-axis ranges from 0 to 6000 in increments of 1000.
[ Image with alt text: Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 6 in increments of 1 and the y-axis ranges from 0 to 6000 in increments of 1000.

Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 60 in increments of 10 and the y-axis ranges from 0 to 6 in increments of 1.
Image with alt text: Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 60 in increments of 10 and the y-axis ranges from 0 to 6 in increments of 1.

Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 60 in increments of 10.
Image with alt text: Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 60 in increments of 10.

Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 6 in unit increments and the y-axis ranges from 0 to 60 in increments of 10.

Answer 1

To determine which graph correctly represents the geometric sequence given by the points:

- (0, 11)
- (1, 16.5)
- (2, 24.75)
- (3, 37.125)
- (4, 55.6875)

We must first analyze the y-values. A geometric sequence means that each term is found by multiplying the previous term by a constant ratio.

In this case, calculating the ratios between consecutive terms:

- From f(0) to f(1): 16.5 / 11 = 1.5
- From f(1) to f(2): 24.75 / 16.5 = 1.5
- From f(2) to f(3): 37.125 / 24.75 = 1.5
- From f(3) to f(4): 55.6875 / 37.125 = 1.5

It’s confirmed that this is a geometric sequence with a common ratio of 1.5.

Now, we will consider the appropriate axis ranges in the graphs:

1. **First Graph**: x-axis from 0 to 6, y-axis from 0 to 6000. This covers the range of the y-values adequately; however, the upper limit seems excessive as our maximum y-value is approximately 55.6875.

2. **Second Graph**: x-axis from 0 to 60, y-axis from 0 to 6. This does not properly represent the data as the entire y-value range is not visible.

3. **Third Graph**: x-axis from 0 to 10, y-axis from 0 to 60. This also does not adequately display the data since the highest y-value (55.6875) would be off the chart.

4. **Fourth Graph**: x-axis from 0 to 6, y-axis from 0 to 60. This graph adequately covers the points as the maximum y-value is 55.6875, which fits within the range.

Among these options, the **fourth graph** is the most accurate representation of the given geometric sequence.