Sum

So this is a common cause of adding numbers together with large numbers (IDK what its called)
Basically, the equation is: Add the First and last term. (in your case it's 2009). Then divide by 2, and multiply by a number of numbers in that said sequence. 
So how do we how many numbers there are in the sequence? We can use the Explicit function: F(x) = 1+3 (x-1), where f(1)=1. This means that 2008-1 = 2007/3 = 669. This means there are 70 terms. So we have 2009/2) x 70. Or 2009 x 35 which is equal to 70315. 
To double-check my work, I used Wolfram Alpha! 

Compute the sum 1 + 4 + 7 + ... + 2005 + 2008.

It is an arithmetic progression

a=1   d=3     L=2008

Tn=a+(n-1)d

2008=1+(n-1)*3

2007/3 = n-1

669=n-1

n=670

sn=n/2(a+L)

Sn=670/2    *(1+2008)

Sn=335  *2009

Sn=673015