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