The Mystery of the Four Consecutive Numbers in the Fibonacci Sequence

The Fibonacci Sequence

The Fibonacci sequence is the sequence of integers 0, 1, 1, 2, 3, 5, 8, 13, 21,…  or 1, 1, 2, 3, 5, 8, 13, 21, …  It is a sequence of numbers that starts with 0 (or 1) and  each number is the sum of the previous two. The sequence first appeared in Liber Abaci, a book written by Leonardo of Pisa, more popularly known as Fibonacci.

fibonacci sequence

The sequence appear in many branches as well as in many form. Take for instance the rectangle above. You can create  a rectangle whose sides are consecutive numbers of the Fibonacci Sequence. The Fibonacci Sequence also appears in the Pascal’s Triangle.

In this post, we discuss another interesting characteristics of Fibonacci Sequence.

The Four Consecutive Numbers

Take any four consecutive numbers in the sequence. Multiply the outer numbers, then multiply the inner numbers. Subtract them. The difference is 1.

Example 1

0, 1, 1, 2, 3, 5, 8, 13, 21

8(2) – 5(3) = 1

Example 2

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

21(5) – 8(13) = 1

Example 3

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

34(8) – 21(13) = 1

Now the question is, is this always true?

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Source: Math Fun Facebook Page

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