examday

/TMUA

In this question, $x_1$, $x_2$, $x_3$, $\ldots$ is an arithmetic progression, all of whose terms are integers.

Let $n$ be a positive integer. If the median of the first $n$ terms of the sequence is an integer, which of the following three statements must be true?

• I The median of the first $n+2$ terms is an integer.
• II The median of the first $2n$ terms is an integer.
• III The median of $x_2$, $x_4$, $x_6$, $\ldots$, $x_{2n}$ is an integer.