GeoGebra

This is a very simple problem on the surface, so simple that an elementary aged student could understand it, yet deep enough to be the focus of graduate level mathematics work. The problem is this: Pick two numbers to start with (Today and Yesterday, Now and Last, $a_2$ and $a_1$. Perform the calculation $\frac{Today + 1}{Yesterday}$ or $\frac{Now + 1}{Last}$ or $\frac{a_{n+1} + 1}{a_n}$ to get a new number. This new number will be referred to as Tomorrow or as Next or as $a_3$. For younger students, it is one day later (Tomorrow is the new Today), or it is one step later (Next is the new Now). Repeat this calculation, continuing to repeat this process until you get to a nice number at which to stop.

Go to Student Worksheet