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
The formula for a geometric sequence is given by f(n) = f(0) * r^n, where f(0) is the first term and r is the common ratio.
In this case, the first term f(0) is 11 and the common ratio r is calculated by dividing each term by the previous term.
Common ratio = 16.5/11 = 1.5
Common ratio = 24.75/16.5 = 1.5
Common ratio = 37.125/24.75 = 1.5
Common ratio = 55.6875/37.125 = 1.5
So, the common ratio is 1.5.
Now we can calculate the other terms using the formula:
f(0) = 11
f(1) = 11 * 1.5^1 = 11 * 1.5 = 16.5
f(2) = 11 * 1.5^2 = 11 * 2.25 = 24.75
f(3) = 11 * 1.5^3 = 11 * 3.375 = 37.125
f(4) = 11 * 1.5^4 = 11 * 5.0625 = 55.6875
The correct graph for the geometric sequence is:
n | f(n)
0 | 11
1 | 16.5
2 | 24.75
3 | 37.125
4 | 55.6875
Note that the values of f(n) increase by a common ratio of 1.5.