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# Fibonacci Sequence

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What is the Fibonacci Sequence?

Nov 28, 2018

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$$\text{The Fibonacci Sequence is a sequence of positive integers }\\ \text{that is defined by the recursive rule}\\ a_0=1,~a_1=1,~a_{n+1}=a_n + a_{n-1}\\ a_2 = a_{1+1} = a_1 + a_0 = 2\\ a_3 = a_{2+1}=a_2 + a_1 = 3 \text{ and so on to obtain }\\ 1, 1,2,3,5,8,13,21, 34 \dots$$

In English each number in the sequence is the sum of the two numbers immediately behind it.

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Nov 28, 2018
edited by Rom  Nov 28, 2018
edited by Rom  Nov 28, 2018

#1
+5172
+3
$$\text{The Fibonacci Sequence is a sequence of positive integers }\\ \text{that is defined by the recursive rule}\\ a_0=1,~a_1=1,~a_{n+1}=a_n + a_{n-1}\\ a_2 = a_{1+1} = a_1 + a_0 = 2\\ a_3 = a_{2+1}=a_2 + a_1 = 3 \text{ and so on to obtain }\\ 1, 1,2,3,5,8,13,21, 34 \dots$$