A factory makes custom sports cars at an increasing rate. In the first month only one car is made, in the second month two cars are made, and so on. with n cars made in the nth month.a) Set up a recurrence relation for the number of cars produced in the first n months by this factory.________________b) How many cars arc produced in the first year?________________c) Find an explicit formula for the number of cars produced in the first n months by this factory.

Solution Step 1:A factory makes custom sports cars at an increasing rate.In the first month only one car is made,in the second month two cars are made,and so on.with n cars made in the monthStep 2:(a) Set up a recurrence relation for the number of cars produced in the first n months by this factory.we have to set up a recurrence relation for number of cars produced in the first n months by this factory.Since the cars produced is 1 greater than previous year,hence the recurrence relation for the number of cars produced in the first n months will be With initial condition