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?
Answer Choices
A. -4\:042\:109
B. -4\:047\:638
C. -4\:038\:094
D. -4\:044\:121
E. -4\:046\:132