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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, …?