To find the function that represents the \(n\)th term of the arithmetic sequence given, we first need to identify the characteristics of the sequence.
The costs of the taxicab rides for 1, 2, 3, and 4 miles are:
- Cost for 1 mile: 5.30
- Cost for 2 miles: 7.80
- Cost for 3 miles: 10.30
- Cost for 4 miles: 12.80
Next, we will determine the first term and the common difference:
- First term (a): The cost for 1 mile is \(5.30\).
- Common difference (d): We can find the common difference by subtracting any two consecutive terms. For instance, the difference between the cost of 2 miles and the cost of 1 mile: \[ d = 7.80 - 5.30 = 2.50 \]
The general form for the \(n\)th term of an arithmetic sequence can be described as: \[ f(n) = a + (n - 1)d \]
Substituting the known values:
- \(a = 5.30\)
- \(d = 2.50\)
We get: \[ f(n) = 5.30 + (n - 1) \cdot 2.50 \] \[ f(n) = 5.30 + 2.50n - 2.50 \] \[ f(n) = 2.80 + 2.50n \]
Thus, the correct function that represents the \(n\)th term of the sequence is: \[ f(n) = 2.80 + 2.50n \]
Therefore, the answer is: f(n) = 2.80 + 2.50n