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 are produced in the first year?

a. I think this would be a_{n = }a_{n-1}+ 1, but something tells me it might be a_{n = }a_{n-1}+ n, I am not sure.

b. Would this just be 1+2+3+4+5+6+7+8+9+10+11+12? Or, plugging in 12 for the above equation?

Thanks.