
Concept explainers
To calculate: The value of ratios of two continuous terms in a fibonacci sequence

Answer to Problem 1AE
The value of ratios of two continuous terms in a fibonacci sequence
Explanation of Solution
Given information:
The fibonacci number sequence is given as
There is one computer programme is also given to run it.
Formula used:
In the fibonacci number sequence the next term is sum of the last two terms, which can be represents by this,
Calculation:
Consider the given computer program and run it in the operating system.
Now, result comes out to be,
Number | n-th Fibonacci Number | f(n)/f(n-1) | f(n-1)/f(n) | f(n)/f(n-1) | Phi=1.618… | f(n-1)/f(n) | Phi=0.618… | |
f-0 | 1 | |||||||
f-1 | 1 | 1 | 1 | 1 | 1.618034 | 1 | 0.618034 | |
f-2 | 2 | 2 | 0.5 | 2 | 1.618034 | 0.5 | 0.618034 | |
f-3 | 3 | 1.5 | 0.666667 | 1.5 | 1.618034 | 0.666667 | 0.618034 | |
f-4 | 5 | 1.666667 | 0.6 | 1.666667 | 1.618034 | 0.6 | 0.618034 | |
f-5 | 8 | 1.6 | 0.625 | 1.6 | 1.618034 | 0.625 | 0.618034 | |
f-6 | 13 | 1.625 | 0.615385 | 1.625 | 1.618034 | 0.615385 | 0.618034 | |
f-7 | 21 | 1.615385 | 0.619048 | 1.615385 | 1.618034 | 0.619048 | 0.618034 | |
f-8 | 34 | 1.619048 | 0.617647 | 1.619048 | 1.618034 | 0.617647 | 0.618034 | |
f-9 | 55 | 1.617647 | 0.618182 | 1.617647 | 1.618034 | 0.618182 | 0.618034 | |
f-10 | 89 | 1.618182 | 0.617978 | 1.618182 | 1.618034 | 0.617978 | 0.618034 | |
f-11 | 144 | 1.617978 | 0.618056 | 1.617978 | 1.618034 | 0.618056 | 0.618034 | |
f-12 | 233 | 1.618056 | 0.618026 | 1.618056 | 1.618034 | 0.618026 | 0.618034 | |
f-13 | 377 | 1.618026 | 0.618037 | 1.618026 | 1.618034 | 0.618037 | 0.618034 | |
f-14 | 610 | 1.618037 | 0.618033 | 1.618037 | 1.618034 | 0.618033 | 0.618034 | |
f-15 | 987 | 1.618033 | 0.618034 | 1.618033 | 1.618034 | 0.618034 | 0.618034 | |
f-16 | 1597 | 1.618034 | 0.618034 | 1.618034 | 1.618034 | 0.618034 | 0.618034 | |
f-17 | 2584 | 1.618034 | 0.618034 | 1.618034 | 1.618034 | 0.618034 | 0.618034 | |
f-18 | 4181 | 1.618034 | 0.618034 | 1.618034 | 1.618034 | 0.618034 | 0.618034 |
It is very clear from the above table that ratio between two continuous successor and Predecessor term is approximate equal to 1.618.
Therefore, the value of ratios of two continuous terms in a fibonacci sequence
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