Question

Which of the following correctly graphs the geometric sequence?

This table shows the relationship between input values (n) and the corresponding output values for the function f(n) showing the values rising by a factor of 1.5 each time, suggesting an exponential function.
n f(n)
𝑓
(
𝑛
)
0 11
1 16.5
2 24.75
3 37.125
4 55.6875

Answer 1

The sequence is geometric with first term 11 and common ratio 1.5, so the rule is

f(n) = 11·(1.5)^n.

This produces the given values:
- f(0)=11
- f(1)=11·1.5 = 16.5
- f(2)=11·(1.5)^2 = 24.75
- f(3)=37.125
- f(4)=55.6875

The correct graph will show discrete points at (0,11), (1,16.5), (2,24.75), (3,37.125), (4,55.6875) (or the continuous exponential curve y=11·1.5^x through those points). It is an increasing, concave-up exponential with horizontal asymptote y=0. Choose the option that matches those points/that shape.