Fibonacci Sequence
The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
The next number is found by adding up the two
numbers before it.
- The 2 is found by adding the two numbers before it (1+1)
- Similarly, the 3
is found by adding the two numbers before it (1+2),
- And the 5 is
(2+3),
- and so on!
Example:
the next number in the sequence above would be 21+34 = 55
It is that simple!
Here is a longer list:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
233, 377, 610, 987, 1597, 2584,
4181, 6765, 10946, 17711, 28657, 46368, 75025,
121393, 196418, 317811, ...
Fibonacci Spiral
Fibonacci Spiral
The Rule
The Fibonacci Sequence can be
written as a "Rule"
(see Sequences and
Series).
First, the terms are numbered
from 0 onwards like
this:
n =
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
...
|
xn =
|
0
|
1
|
1
|
2
|
3
|
5
|
8
|
13
|
21
|
34
|
55
|
89
|
144
|
233
|
377
|
...
|
So term number 6 is called x6 (which equals 8).
Example: the 8th term is
the 7th term plus the 6th term: x8 = x7 + x6 |
So we can write the rule:
The Rule is xn = xn-1 + xn-2
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