, 2011

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) $-4\,046\,132$