Using Excel to Explore the Fibonacci Sequence
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.