# 2011 AIME II Problems/Problem 5

Problem:

The sum of the first 2011 terms of a geometric sequence is 200. The sum of the first 4022 terms is 380. Find the sum of the first 6033 terms.

Solution: (somebody please confirm)

Since the sum of the first 2011 terms is 200, and the sum of the fist 4022 terms is 380, the sum of the second 2011 terms is 180. This is decreasing from the first 2011, so the common ratio (or whatever the term for what you multiply it by is) is less than one.

(this section probably incorrect:) Because it is a geometric sequence and the first 2011 terms is 200, second 2011 is 180, then the third is 140? If so, 200+180+140=520

Sum of the first 6033 is 520.