Tag Archives: Fibonacci

25.Fibonacci sequence to contain 1000 digits

The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.

Hence the first 12 terms will be:

F1 = 1   F2 = 1   F3 = 2   F4 = 3  F5 = 5  F6 = 8  F7 = 13  F8 = 21  F9 = 34  F10 = 55  F11 = 89  F12 = 144

The 12th term, F12, is the first term to contain three digits.  What is the first term in the Fibonacci sequence to contain 1000 digits? Read more of this post

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Fibonacci Sequence

Each new term in the Fibonacci sequence is generated by adding the previous two terms.  By starting with 1 and 2, the first 10 terms will be:  1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

By considering the terms in the Fibonacci sequence whose values do not exceed four million,  find the sum of the even-valued terms.

In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144 (sequence A000045 in OEIS).

By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the
sum of the previous two.

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