My New Account

I recently opened a new bank account and ended up with $25 after the first month.  Six months later, I noticed that I had $235 in the same account.  The bank teller looked at my statements and commented that the amount of money in the account at the end of each month was the sum of the preceding two months.  What was the account balance after each month?

Month	Account Balance
1	$25
2
3
4
5
6	$235

I really like this type of problem for students of any age who we want to start thinking algebraically. 

How can your students move from guess-and-check to algebraic methods of solving this type of problem?