Unattributed TMUA Mock Set A Paper 2 · Question 20

Arrange the positive integers into a triangular array as shown in the left diagram. Then, following the given rules, take out the odd numbers in even rows and the even numbers in odd rows to obtain the triangular array shown in the right diagram. Next, arrange the numbers from the right diagram in ascending order to form a sequence $\{a_n\}$ . If $a_n=2011$ , then what is the value of $n$ ?

\begin{array}{c} 1\\2\quad3\quad4\\5\quad6\quad7\quad8\quad9\\10\ 11\ 12\ 13\ 14\ 15\ 16\\17\ 18\ 19\ 20\ 21\ 22\ 23\ 24\ 25\\26\ 27\ 28\ 29\ 30\ 31\ 32\ 33\ 34\ 35\ 36\\\cdots \end{array}\quad\longrightarrow\quad\begin{array}{c} 1\\2\quad4\\5\quad7\quad9\\10\quad12\quad14\quad16\\17\quad19\quad21\quad23\quad25\\26\quad28\quad30\quad32\quad34\quad36\\\cdots \end{array}

1024

1025

1026

1027

1028

1029

examday

Unattributed TMUA Mock Set A Paper 2 · Q20