## The Fibonacci Sequence can be generated by, f(n) = f(n-1) + f(n-2).

We can determine f(n) if we are given the two pervious terms, f(n - 1) & f(n - 2).

f(n) is the sum of these two terms.

## Use excel to generate the Fibonacci Sequence, starting with f(0)=1 and f(1) = 1.

## Use excel to construct the ratio of each pair of adjacent terms in the Fibonacci Sequence. Do the same for every second term and every third term.

## What observations do you make?

## First, lets look at the column that contains the ratios of adjacent terms. As n increases, f(n) is getting closer and closer to 1.618.

## 1.618 or is known as the Golden Ratio.

## Looking at the column that contains the ratios of all the second terms, we see that f(n) is approaching 2.618 as n is increasing.

## The third column, which contains the ratios of all the third terms, is approaching as n increases.

## Lets repeat the same process, but this time starting with f(0) = 1 and f (1) = 3. This is called the Lucas Sequence.

## Once again, the columns approach , , & .

## Lets see if this holds for other arbitrary integers.

I decided to start with f(0) = -3 and f(1) = 6.## Again, the ratios converge on powers of the golden ratio.

We can conclude that the ratio of every nth term converges to .## Click here to return to Lacy's homepage.