Question

Which function represents the nth term of the arithmetic sequence that shows the costs, in dollars, of riding 1, 2, 3, and 4 miles (and so on) in a certain taxicab, for n = 1, 2, 3, 4, ... ?

A) f(n) = 2.80 + 2.50n.
B) f(n) = -2.50 + 7.80n.
C) f(n) = 5.30 + 7.80n.
D) f(n) = 5.30 + 2.50n.

Answer 1

The function that represents the nth term of the arithmetic sequence showing the costs of riding different distances in a taxicab is f(n) = 5.30 + 2.50n.

Step-by-step explanation:

In this case, the function that represents the nth term of the arithmetic sequence showing the costs of riding 1, 2, 3, and 4 miles in a certain taxicab is option D) f(n) = 5.30 + 2.50n.

To determine the nth term, we use the formula: f(n) = a + (n-1)d.

In the given options, the constant term is $5.30, which represents the cost of riding 0 miles (because when n = 1, we have 0 miles). The common difference is $2.50, which represents the increase in cost as the number of miles increases by 1.

For example, when n = 1, the cost of riding 1 mile is $5.30 + ($2.50 * 1) = $7.80. Similarly, when n = 2, the cost of riding 2 miles is $5.30 + ($2.50 * 2) = $10.30, and so on.