This assignment asks you to explore the fibonacci numbers and similar sequences. IMHO (if unfamiliar with this acronym try googling: “define IMHO”), the best way to do all of the following is to use Excel. The attach to the printout a description of what you observed. If you don’t use Excel, tabulate your calculations neatly and be sure to give your observations and conclusions. Your Excel results will be easier for me to understand if you put column headings above the numerical calculations. Lastly don’t forget to include your name.

1. Instead of using 1, 1 as the first two terms of the Fibonacci series, try starting with 2, 1 (NOTE: NOT 1, 2) . As in the Fibonacci series, define each term as the sum of the previous two. Generate the first 10 terms of this new sequence. As we did with the Fibonacci series, calculate the ratios of successive terms. What number do these ratios seem to approach? Now try two other starting numbers and repeat the above. That is generate the new sequence and the ratios. Summarize your observations in a short paragraph.

2. Here are two more experiments you can do quickly using Excel. Try calculating the difference of the squares of two Fibonacci numbers that are two apart. If we have: 1 1 2 3 5 8 13, we want to calculate:

2²-1² 3²-1² 5²-2² ...

Can you describe these numbers in terms of the Fibonacci numbers?