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**Assignment 12**

**Using Excel to Explore the
Fibonacci Sequence**

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Enter a 1 in cells A1 and
A2. In cell A3 type =A1+A2. Click on cell A3. The outline of the cell should now be
highlighted. Place the pointer on
the bottom right corner of the cell.
The pointer should turn into a square with arrows on two corners. Click and hold down the button on the
mouse. Drag the box down about 30
rows. Release the mouse
button. The cells A1 through A30
should now represent the Fibonacci sequence.

Now let’s look at
the ratio of each pair of adjacent terms.
In cell B2 type =A2/A1.
Just like before, highlight the cell and click and hold on the bottom
right corner. Drag the formula
down.

As you can see, the ratio
of adjacent terms quickly converges to the **golden
ratio**.

Now let’s
investigate the ratio of every second term. In cell B3 type =A3/A1. Just like before, highlight the cell
and click and hold on the bottom right corner. Drag the formula down.

As you can see, the ratio
of every second term quickly converges to the square of the golden ratio.

Let’s see what
happens for the ratio of every third term. What do you think it will be?

It should be no surprise
that the ratio of every third term is the golden ratio cubed.

It appears that the ratio
of every nth term of the Fibonacci sequence is the golden ration raised to the
n power.

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