Generate a Fibonnaci sequence in the first column of your spreadsheet using f(0) = 1, f(1)= 1,

Construct the ratio of each pair of adjacent terms in the Fibonnaci sequence. What happens as n increases?

What about the ratio of every second term? Now what happens as n increase?

Continue this progression and find the ratio of every third, fourth, and fifth term. Investigate and interpret mathematically any patterns that arise. Discussion.

If f(0)=1 and f(1) = 3, then your sequence is a Lucas Sequence. Look at the ratio of successive terms in this series. What do you notice?

Explore sequences where f(0) and f(1) are some arbitrary integers other than 1. What do you notice about the ratios here?