Our task in this assignment is to develope a spreadsheet of values. I will begin by generating a Fibonnaci sequence in this first column. To view spreadsheet info Click here.

Question: What happens as the ratio of successive terms increases?

Well, we can see from our spreadsheet that as our Fibonnaci sequence increases, the ratio of successive terms approaches the golden ratio of 1.6180.....

Let's see what happens when we take the ratio of every second term:

By looking at our spreadsheet we can clearly see that our third column, which is the ratio of every second term, will approach 2.1680.......Let's do every third term.

We can see that our fourth column, which is the ratio of every third term, will approach 4.23606.... To view spreadsheet Click here.

Now, let's generate a Lucas Sequence (i,e. 1,3,4,7,11,18,..........)

Question: What happens as the ratio of successive terms increases?

Well, from our spreadsheet we see that our sequence approaches the golden ratio 1.6180...../ just like we saw with the Fibonnaci Sequence.

Question: What happens if our f(0)=3 and our f(1)=7?

After we generate this sequence, we can see that the sequence of the ratio of successive terms also approaches the golden ratio 1.6180......To view Click here.

It appears that for any two numbers f(0) and f(1) the ratio of successive terms will approach the golden ratio!