1996 AHSME Problem 24

The sequence 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2,\ldots consists of 1’s separated by blocks of 2’s with n 2’s in the n^{th} block. The sum of the first 1234 terms of this sequence is

\text{(A)}\ 1996\qquad\text{(B)}\ 2419\qquad\text{(C)}\ 2429\qquad\text{(D)}\ 2439\qquad\text{(E)}\ 2449

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.