Tag Archives: Fibonacci

Project Euler: Problem 25

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The Fibonacci sequence is defined by the recurrence relation:

F_n = F_{n-1} + F_{n-2}, where F_1 = 1 and F_2 = 1.

Hence the first 12 terms will be:

F_1 = 1 \\ F_2 = 1 \\ \ldots \\ F_{11} = 89 \\ F_{12} = 144

The 12th term, F_{12}, is the first term to contain three digits.

What is the first term in the Fibonacci sequence to contain 1000 digits?

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Project Euler: Problem 2

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Alright, next Project Euler problem:

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, …

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

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