MATH SOLVE

3 months ago

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# What is the fibonacci sequence who invented it and what is it used for

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Answer:Read the explanationStep-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