The city buses that run in your neighborhood stop every 12 minutes. The first bus arrives at 5:00 a.m. for passengers. You get to the bus stop at 8:37am. How long will you have to wait for a bus? Please answer this question using the explicit formula of an arithmetic sequence.

number of minutes between 5:00 and 8:37 = 3hr37' = 247

that is 20*12 + 7
so you need to wait 5 minutes

Did you know?

Did you know that arithmetic sequences can also be used to determine the waiting time for city buses? In an arithmetic sequence, the first term is given, and the common difference indicates the time interval between each subsequent term. In this case, the first bus arrives at 5:00 a.m., and the time interval between each bus is 12 minutes. So, the explicit formula for the arithmetic sequence representing the bus arrival times would be: An = 5:00 + (n-1) * 12, where An represents the arrival time of the nth bus in minutes since midnight. To calculate the waiting time at 8:37 a.m., we need to find the value of n for which An is the closest but smaller than 8:37. By substituting the given values into the formula, we can solve for n. Once we have n, we can calculate the waiting time by subtracting the arrival time of the previous bus (An-1) from 8:37. This will give us the waiting time in minutes.