1. Wrote down two numbers - the first and the second. Added the second to the first - got the third, added the third to the second - got the fourth, and so on. The sum of the first six numbers is 2008. What is the fifth number?
Answer: 502. Solution: Let the first number be $a$, the second - $b$. Then the third number is $a+b$, the fourth $-a+2b$, the fifth $-2a+3b$, the sixth $-3a+5b$, and the sum of all six numbers is $8a+12b$. Thus, the fifth number is a quarter of the sum of all six numbers, that is, $2008: 4=502$.

Grading Guidelines. Answer without justification - 0 points. Answer obtained by considering a numerical example - 0 points. Noted that $2a+3b=(8a+12b)/4$, but division of 2008 by 4 is incorrect - 4 points.