Question

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.

Answer 1

tough one... not sure how anyone can solve this without using computer :/

Answer 2

This took me about about 5 minutes, but it seems that there is a nifty trick for the sum of a fibonnaci sequence. You can prove this (as I did), but it becomes evident that the sum of the first x fibonnaci numbers is the (x+2)th fibonnaci number -2. Therefore, your new problem is to find the fibonnaci number that is the second fibonnaci number greater than 4 million (a much easier problem). Thankfully, this is not so difficult to find (it being only the 35th fibonnaci number at 9227465). Therefore your answer is 9227463!

Answer 3

@daniel9876000 looks cute !! :))

Answer 4

thnx for the reply!