I'm preparing for an upcoming exam on Discrete Maths, and I've come across the following past exam question which I don't quite understand:
An ATM dispenses only \$20 and \$50 notes. Let M be the set of amounts of money that the ATM can dispense
Write down a recursive definition of M
As I understand it, a recursive statement is something in the form of: $a_{n} + a_{n-1} - 5a_{n-2} = 0$
I do understand what a recurrence relation is basically - and I know how to solve a recurrence given initial statements $a_{0}$ and $a_{1}$ but I'm finding these types of questions a bit confusing as there doesn't seem to be any standard algorithm or technique for it
What confuses me even more with this question is the answer that is given is:
If \$m belong to M then \$(m+20)$ belong to M and \$(m+50)$ belong to M
Which is not really in the form that I'm more familiar with - but I suspect it can also be rewritten in the normal form?