A term in the Fibonacci Sequence is created by adding the previoius two terms in the sequence together. Mathematicians find the sequence interesting because after a while, the ratio of the two last numbers converges to a particular value, called the golden ratio.

Doing all the calculations can be kind of boring, so this web page will let you pick the starting numbers, and it will calculate the sequence for you, so that you can just focus on seering what's the same and what's different when you change things. The equation on the left shows the sum of the previous two terms (can you tell where the numbers come from?) The equation on the right shows the ratio.

The Fibonacci Sequence starts with 1 & 1 as the two starting numbers. What happens if you use the same rules, but make the first number a 0. How about the second number? what happens if you pick two numbers that appear later in the sequence, say 3 & 5? Do parts of the sequence still look familiar? what happens if you use a negative number?

What happens if the two starting numbers don't match any of the numbers in the Fibonacci Sequence? Does that affect what the ratio converges to?

Can you find anything else interesting about this series?

Compare the ratios you found here with the ratios from the Golden Rectangle and the Golden Triangle pages. When you're done with those, you may wonder where that golden ratio comes from, anyway?.