Answer:
Read the explanation
Step-by-step explanation:
- 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
# Example:
- The 2 is found by adding the two numbers before it (1+1)
- The 3 is found by adding the two numbers before it (1+2),
- The 5 is (2+3) and so on
- The rule of it is x(n) = x(n-1) + x(n-2) where
# x(n) is term number ⇒ n
# x(n-1) is the previous term ⇒ (n-1)
# x(n-2) is the term before that ⇒ (n-2)
- Example: the 8th term is the 7th term plus the 6th term:
x(8) = x(7) + x(6)
# Note: When we take any two consecutive Fibonacci Numbers,
their ratio is very close to the Golden Ratio φ
- The Golden Ratio φ is approximately 1.618034...
- We can calculate any Fibonacci Number using the Golden Ratio:
x(n) = [φ^n - (1 - φ)^n]/√5
- The answer is a whole number, exactly equal to the addition of the
previous two terms.
# There is an interesting patterns in Fibonacci sequence:
every nth number is a multiple of x(n)
- Example:
* x3 = 2 ⇒ every 3rd number is a multiple of 2 (2, 8, 34, 144, 610, ...)
* x4 = 3 ⇒ Every 4th number is a multiple of 3 (3, 21, 144, ...)
* x5 = 5 ⇒ Every 5th number is a multiple of 5 (5, 55, 610, ...)
- The man who invented it.
His real name was Leonardo Pisano Bogollo, and he lived between
1170 and 1250 in Italy.
- Fibonacci was his nickname
- Fibonacci sequence is it used for:
# Reflects patterns of growth spirals (a spiral curve , shape , pattern ,
object) found in nature
# It is the closest approximation in integers to the logarithmic spiral
series, which follows the same rule as the Fibonacci sequence
