Question

Lee is staying at a hotel the cost of the first night is 240$ the cost for each night after that is 210$ let y represent the total cost of staying at the hotel for x nights
Which type of sequence does the situation represent

A the situation represents an arithmetic sequence because the successive y values have a common difference of 210

B the situation represents a geometric sequence because the successive y values have a common ratio of 210

C the situation represents an arithmetic sequence because the successive y values have a common difference of 30

D the situation represents a geometric sequence because of the successive y values have a common ratio of 30

Answer 1

Let's write the function that represents the problem:
 ax = 210x + 240
 We are going to evaluate the first five nights:
 a0 = 210 * (0) + 240 = 240
 a1 = 210 * (1) + 240 = 450
 a2 = 210 * (2) + 240 = 660
 a3 = 210 * (3) + 240 = 870
 a4 = 210 * (3) + 240 = 1080
 We then have the following terms:
 240, 450, 660, 870, 1080
 We observe that the common difference of the terms is:
 210
 Therefore, since they have the same common difference, we are facing an arithmetic sequence.
 Answer:
 A the situation represents an arithmetic sequence because of the successive and values have a common difference of 210