**A recursive sequence **is a sequence defined by the inductive method, and it is also one of the commonly used methods of defining a sequence. The sequences introduced in Experiment and Experiment are all recursive sequences.

Observe the changing trend of the Fibonacci sequence:

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Fibonacci ( year year) was an Italian mathematician and the first person in the West to study the Fibonacci sequence. The Fibonacci sequence was introduced by the mathematician Leonardo Fibonacci using the example of rabbit reproduction, so it is also called the "**rabbit sequence**" . It has direct applications in modern physics, quasicrystal structures, chemistry and other fields. For this reason, the American Mathematical Society has research results in this area.

Using calculation software, it is easy to calculate the first terms of the Fibonacci sequence:

The scatter plot is shown in the figure.

Interestingly, for such a sequence that is entirely natural numbers, the general formula is expressed in irrational numbers, that is

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The Fibonacci sequence is also called the golden ratio sequence. As approaches infinity, the ratio of the previous item to the next item in the sequence becomes closer and closer to the **golden **ratio .

[ Detailed explanation of the experiment ]