The Fibonacci Sequence - Holy Cross of Davao College - PDF

The Fibonacci Sequence LEONARDO FIBONACCI ❖ Leonardo of Pisa, also known as Fibonacci, is one of the best known mathematicians of medieval Europe. ❖ In, 1202, after a trip that took him to several Arab and Eastern countries, he wrote the book Liber Abaci.  The Fibonacci Sequence exhib...

The Fibonacci Sequence LEONARDO FIBONACCI ❖ Leonardo of Pisa, also known as Fibonacci, is one of the best known mathematicians of medieval Europe. ❖ In, 1202, after a trip that took him to several Arab and Eastern countries, he wrote the book Liber Abaci.  The Fibonacci Sequence exhibits a certain numerical pattern which originated as the answer to the famous rabbit problem. A man put a male-female pair of newly born rabbits in a field. Rabbits take a month to mature before mating. One month after mating, females give birth to one male-female pair and then mate again. No rabbits die. How many rabbit pairs are there after one year? ❖ If we are going to write the number of pairs of rabbits in a sequence after 5 months, it will look like this, 1, 1, 2, 3, 5, ……. ❖ Fibonacci discovered that the number of pairs of rabbits of any month after the first two months can be found by adding the numbers of pairs of rabbits in each of the two previous months. ❖ The recursive definition of Fibonacci sequence: ❖ Let the notation Fₙ represent the nth Fibonacci number, then the numbers in the Fibonacci sequence are given by the following: ❖ F₁ = 1, F₂ = 1, and Fₙ = Fn-1 + Fn-2, where n > 3 F₁ = 1, F₂ = 1, and Fₙ = Fn-1 + FExample: n-2 ❖ Using the recursive formula for the Fibonacci sequence, Find the following: a. F₃ b. F ₄ c. F ₅ d. F ₆ Example: Find the 9th term of a Fibonacci Sequence using the Binet’s Formula. Just use the six decimal places of the Golden Ratio (1.618034). Try to answer: Find the 25th term of a Fibonacci sequence using the Binet’s formula. (You can use your calculator to solve easily) Thank you!