Question 24
The sequence $$
\begin{gathered} 1,2,1,2,2,1,2,2,2,1,2,\\ 2,2,2,1,2,2,2,2,2,1,2,\ldots \end{gathered}
$$ 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
\begin{gathered} 1,2,1,2,2,1,2,2,2,1,2,\\ 2,2,2,1,2,2,2,2,2,1,2,\ldots \end{gathered}
$$ 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