linkProblem 2 - Even Fibonacci numbers

linkQuestion

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.

linkSolution

euler_002.py
1linkdef generate_fibonacci_sequence(term_limit, first_term, second_term):

2link    sequence = [first_term, second_term]

3link    while True:

4link        next_number = sequence[-1] + sequence[-2]

5link        if next_number < term_limit:

6link            sequence.append(next_number)

7link        else:

8link            break

9link

10link    return sequence

11link

12linkfour_million_sequence = generate_fibonacci_sequence(4000000, 1, 2)

13linkprint(sum([n for n in four_million_sequence if n % 2 == 0])) # // @see [List Comprehension](https://www.programiz.com/python-programming/list-comprehension)

linkDiscussion

• Let us first start by creating a function that generates a Fibonacci sequence. This accepts three parameters:
  • term_limit: the maximum number in the sequence
  • first_term: the first number in the sequence
  • second_term: the second number in the sequence
• The first and second terms are put into a list sequence
• We go in this loop until next_number reaches the term_limit.
  • The next number in the sequence is calculated by adding the last two numbers in the sequence, which is sequence[-1] and sequence[-2] respectively.
  • Check if next_number is less than the term_limit.
    • If it is, then append it to sequence.
    • If it is not, then stop the loop.
• Running this function will show:

  1linkprint(generate_fibonacci_sequence(10, 0, 1))
  
  2link[0, 1, 1, 2, 3, 5, 8]
  
  

• Another example:

  1linkprint(generate_fibonacci_sequence(90, 1, 2))
  
  2link[1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
  
  

• Generate a Fibonacci sequence whose values do not exceed four million and that it starts with 1 and 2.
• We get the sum of all even numbers in the sequence by using list comprehension.
  This is shorthand for:chevron_right

  1linktotal = 0
  
  2linkfor n in four_million_sequence:
  
  3link  if n % 2 == 0:
  
  4link  total += n
  
  

linkAnswer