Here is the Problem 2 of Project Euler. It requires finding EVEN fibonacci sequence terms till 4 million and adding them up.

As the terms in the Fibonacci sequence grow in magnitude with each consecutive number, we wouldn’t have a lot many number to be added to sum. So an “int” sized variable would be able to hold the sum.

There are two parts of this problem:

1. Finding if the fibonacci sequence. We generate fibonacci sequence as follows:

Starting with two fibonacci numbers, fibonacciNumber1 = 0, fibonacciNumber2 = 1

nextFibonacciNumber = fibonacciNumber1 + fibonacciNumber 2

2. Checking if the fibonacci number generated is even or not. If its even add it to sum.

if(x%2 == 0) sum = sum + x;

**Java implementation of above is as follows:**

`/*PROBLEM: By considering the terms in the Fibonacci`

`sequence whose values do not exceed four million, `

`find the sum of the even-valued terms. */`

`//OUTPUT: 4613732`

`class`

AddFibNum`{`

` ``int`

sum;

` ``int`

x=0,y=`1`

;

` ``void`

findFib`(`

`)`

`{`

` ``int`

temp = `0`

;

` ``while`

`(`

x<`4000000`

`)`

`{`

` temp = x + y;`

` x=y;`

` y = temp;`

` findSum``(`

`)`

;

` ``}`

` printSum``(`

`)`

;

` ``}`

` ``void`

findSum`(`

`)`

`{`

` ``if`

`(`

x%`2`

== `0`

`)`

` sum = sum + x;`

` ``}`

` ``void`

printSum`(`

`)`

`{`

` System.out.println``(`

`"The sum is :"`

+sum`)`

;

` ``}`

`}`

`class`

Test2`{`

` ``public`

`static`

`void`

main`(`

String `[`

`]`

args`)`

`{`

` AddFibNum a = ``new`

AddFibNum`(`

`)`

;

` a.findFib``(`

`)`

;

`}`

`}`

It can be solved in a much efficient manner by taking into consideration the recursive pattern.

Thanks. Keep Coding.