The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding numbers, starting with 0 and 1. This results in the sequence being 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. The ratio of consecutive Fibonacci numbers approaches the golden ratio as the numbers grow larger. Fibonacci numbers were named after the Italian mathematician Leonardo of Pisa, but the concept was described even earlier in ancient Indian mathematics from as early as 200 BC. The document provides an activity to complete longer examples of the Fibonacci sequence.

1. FIBONACCI NUMBERS
ALAN S. ABERILLA

2. In mathematics, the Fibonacci numbers, commonly
denoted Fn, form a sequence, called the Fibonacci
sequence, such that each number is the sum of the two
preceding ones, starting from 0 and 1. That is, FO = 0,
F1 = 1 and Fn = Fn-2 + Fn-2 and for n > 1.
The beginning of the sequence is thus:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.
In some other books, FO = 0, so that the sequence starts
F1 = F2 = 1.

3. Fibonacci numbers are strongly related to the golden ratio:
Binet’s formula expresses the nth Fibonacci number in terms
of n and the golden ratio, and implies that the ratio of two
consecutive Fibonacci numbers tends to the golden ratio
as n increases.
Fibonacci numbers are named after Italian mathematician
Leonardo of Pisa, later known as Fibonacci. In his 1202
book Liber Abaci, Fibonacci introduced the sequence to
Western European mathematics, although the sequence had
been described earlier in Indian Mathematician as early as
200 BC in work by Pingala on enumerating possible patterns
of Sanskrit poetry formed from syllables of two lengths.

4. ACTIVITY 6:
Complete the sequence bellows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ____,
377, 610, 987, _____, _____, 4181, _____, ______,
17711, _____, ______, _______, ______, ______,
317811
Use short bond paper (handwritten or
computerized) – utilize the folder of assignment
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