# Thread: Recursive and Explicit Equations...How to Write Them?

1. ## Recursive and Explicit Equations...How to Write Them?

Hi,

I have been struggling with understanding these equations, searching for a way to simplify them. My professor makes them seem impossible, and I don't understand her teaching methods...so going to her for help, isn't really an option. I have been researching for a different way to do them, but I just cannot figure it out. Help!!

Here is a problem I am working on...if you could give me an example of something similar (I would rather find the answer to this one on my own!).

Suppose that a population grows according to a linear growth model. The initial population is 200, and it grows by 25 every month.
--Write a recursive equation that can be used to find the population at the end of any month.
--Write an explicit equation that can be used to find the population at the end of any month.

Thank you for any help you can give me!!!

2. A recursive formula is going to define a future term by previous ones. Something like $\displaystyle x_{n+1}=x_{n}+x_{n-1}$. That's the Fibonacci sequence. It relies though on knowing previous terms explicitly.

An explicit formula for your example would input the number of months from the beginning and output the population. I'd call it P(m). To do this, look for a pattern in the way each month's total ends up being. You can then generalize the population for any month.