Library / CEMC Gauss (Grade 8) /466 of 525

CEMC Gauss (Grade 8), 2011

Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

Daryl first writes the perfect squares as a sequence $1, 4, 9, 16, 25, 36, 49, 64, 81, 100, \ldots$ After the number 1, he then alternates by making two terms negative followed by leaving two terms positive. Daryl's new sequence is $1, -4, -9, 16, 25, -36, -49, 64, 81, -100, \ldots$ What is the sum of the first 2011 terms in this new sequence?

(A) $-4\,042\,109$ (B) $-4\,047\,638$ (C) $-4\,038\,094$ (D) $-4\,044\,121$ (E) $-4\,046\,132$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.