Q: Why is the sequence 1 1 2 3 5 8 13 so beautiful?

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The spacing is 6 1+6=7 7+6=13 13+6=19 19+6=25 so the missing number in the sequence is 13

Fibonacci sequence Fibonacci sequence

8 and 34 Alterative answer: Convensionally, the Fibonacci sequence starts with two 1s. So 1 and 8 are missing.

arithmetic

Usually a sequence is written using subscripts to represent a number in the sequence. Example: The sequence 1, 7, 13, 19, 25 is by adding six each time. So we can write it as: a_0 = 1 a_1 = 7 a_(n) = a_(n-1) + 6, where n is the subscript.

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The Fibonacci sequence starts with 0, 1. Each subsequent number is the sum of the two preceding ones. So the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, and so on.

The spacing is 6 1+6=7 7+6=13 13+6=19 19+6=25 so the missing number in the sequence is 13

Fibonacci Sequence

Fibonacci sequence Fibonacci sequence

8 and 34 Alterative answer: Convensionally, the Fibonacci sequence starts with two 1s. So 1 and 8 are missing.

arithmetic

Usually a sequence is written using subscripts to represent a number in the sequence. Example: The sequence 1, 7, 13, 19, 25 is by adding six each time. So we can write it as: a_0 = 1 a_1 = 7 a_(n) = a_(n-1) + 6, where n is the subscript.

The pattern is plus 7. So the next number used to be 1.

1, 1 are the first two numbers in the sequence; so, that's where you begin. In the Fibonacci sequence, you add numbers. Each sum is added to the previous largest number, to make the next number in the sequence. So, adding the first two numbers; 1 + 1 = 2. Then, as 2 was the resulting sum; and one was the last largest number, you add them. 1 + 2 = 3. And so on... The first ten numbers in the sequence are; 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. It continues like this, indefinitely.

Paris - 1979 America the Beautiful 1-13 was released on: USA: 1980

121

13, 21 - it is the Fibonacci sequence