Consider the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ....
The first two numbers are 1 and 1. When you add these numbers, you get 2 = 1+1, which becomes the third number in the sequence. When you add the second and third numbers, you get 3 = 1+2, which becomes the fourth number in the sequence. When you add the third and fourth numbers, you get 5 = 2+3, which becomes the fifth number in the sequence; and so on to generate the sequence.
Write a short Excel program that generates the first 50 numbers of the Fibonacci sequence, using 1 and 1 as the first two numbers to start the sequence. Put these numbers in Column A in Excel. Also, in the next column in Excel (Column B), divide each number in the sequence by the previous number in the sequence. This column is a new sequence of numbers. Start Column B in Row 2.
To what number does the sequence of the quotients in Column B converge? Use the 2-D Bar Chart tool in Excel to graph the first 10 ratios in Column B.