(Solved Homework): Using Matlab The Fibonacci sequence defined by

Using Matlab

The Fibonacci sequence defined by

fib 1. 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

where the Nth term, is given by

As N increases, the ratio of two adjacent terms in the sequence approaches The Golden Ratio, ϕ:

Write a function that accepts a single input that is the tolerance, TolGR for the Golden Ratio calculation. Use a loop to generate Fibonacci numbers until the error in subsequent calculations of ϕ, defined by

is less than or equal to TolGR. Your function should output three scalar values, in order:

The final value of the Golden Ratio (a double precision number)

The largest Fibonacci number generated (32-bit unsigned integer datatype)

The number of terms, N, required to meet the tolerance (8-bit unsigned integer datatype).

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Expert Answer

Code:

%Define a function Gratio

function Gratio(TolGR)

%Declare variable

fib1 = 1;

%Declare variable

fib2 =1;

%Compute phi1

phi1 = fib2/fib1 ;

%Declare variable

n = 3 ;

%Loop infinite

while true

%Compute fib3

fib3 = fib1+fib2;

%Assign value

fib1=fib2;

%Assign value

fib2 = fib3;

%Compute ratio

phi2 = fib2/fib1

%compute error

err = abs(phi2-phi1)

%If error value is less than tolerance

if err<TolGR

%Break

break

%End

end

%Assign value

phi1 = phi2;

%Update value

n=n+1;

%End

end

%Display value

disp(phi2)

%Display result

fprintf(‘The Fibonacci sequence to %d terms isn’,n)

%Display result

fprintf(‘%g ‘,fib3)

%Display new line

fprintf(‘n’)

%End

end

%Call method

Gratio(0.05)

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