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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Recursively Defined Sequences

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Exercise 4 Page 313

The sequence described in Example 1 and Example 2 is also known as The Fibonacci Sequence.

See solution.

Practice makes perfect

The Italian mathematician Leonardo Fibonacci, known also as Leonardo Pisano and Leonardo of Pisa, is best known for the recursive sequence shown in Example 2, defined by the recursive rule a_n = a_(n-1)+a_(n-2). Its first terms are a_1=1 and a_2=1.

Fibonacci numbers in the Fibonacci sequence

This is why this sequence is also known as The Fibonacci Sequence. He used it to describe how pairs of rabbits increase as they multiply under the conditions described in Example 1. It was later discovered that this sequence is related to the golden ratio. It appears in nature, for example, in the spirals of sunflower heads.

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320