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Fibonacci Sequence (Definition, Formula and Examples)

Fibonacci Sequence: A Brief Discussion

It is a set of numbers that starts with one (1) or a zero (0), followed by one (1), and the sequence proceeds by following a rule –each Fibonacci number is equal to the sum of the preceding two numbers. Fibonacci sequence is named after Leonardo Pisano, also known as Fibonacci; an Italian mathematician who lived from 1170-1250. The Fibonacci sequence is a result of a mathematical problem about breeding of rabbits, posed in Leonardo Pisano’s book Liber Abaci (Book of the Abacus) published in 1202.

The Fibonacci Sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … OR 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … In mathematical sentence, a term in the Fibonacci sequence can be found by using the rule: .


Examples of Mathematical Problems on Fibonacci Sequence

Using the sequence, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … the first term is 1, the second term is 1, the third term is 2, the fourth term is 3, and so on.

Example 1: What is the 6th term of the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …? ( See the solution in the photo below.)


The given rule ( Fn = Fn-1 + Fn-2 ) of the Fibonacci sequence requires us to know or identify the two preceding terms to find the nth term. This formula is not quite convenient to use when we are asked to find the other terms in the sequence such as 16th or 100th term. With this matter, we can use the formula:


Example 2: What is the 16th term in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …?


Who is Leonardo Pisano "Fibonacci" ?

Leonardo Pisano, also known as Fibonacci, Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano, was an Italian Mathematician from Pisa who introduced the Fibonacci sequence. He was born around 1170 to an Italian merchant and customs official named Guglielmo who directed a trading post in Bugia, Algeria. Leonardo Pisano as a young boy traveled with his father, and learned the Hindu-Arabic numeral system when he was in Bugia, Algeria. As Leonardo Pisano traveled around the coast of Mediterranean, he met many merchants and learned about systems of arithmetic. It was during that time when he learned that Hindu-Arabic system is more convenient to use than the Roman numerals. He has published book in 1202 titled Liber Abaci which means Book of Abacus or the Book of Calculation. This book paved the way to the popularization of the Hindu-Arabic Numerals in Europe. The book also posed the mathematical problem on the growth of population of rabbits based on idealized assumptions where the concept of Fibonacci sequence started.

Leonardo Pisano's other books known today are Practica Geometriae (1220), Flos numbers (1225), and Liber Quadratorum (1225).

Leonardo Pisano also known as "Fibonacci"


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