10. Let $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ be a sequence of real numbers satisfying $a_{n+1} = \frac{n(n+1)}{2} - a_{n}$ for all positive integers $n$. Which of the following options are correct? (1) If $a_{1} = 1$, then $a_{2} = 1$ (2) If $a_{1}$ is an integer, then every term of the sequence is an integer (3) If $a_{1}$ is irrational, then every term of the sequence is irrational (4) $a_{2} \leq a_{4} \leq \cdots \leq a_{2n} \leq \cdots$ (where $n$ is a positive integer) (5) If $a_{k}$ is odd, then $a_{k+2}, a_{k+4}, \ldots, a_{k+2n}, \ldots$ are all odd (where $n$ is a positive integer)
& 2，3，4 & & 22 & 4 & & 32 & 4
10. Let $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ be a sequence of real numbers satisfying $a_{n+1} = \frac{n(n+1)}{2} - a_{n}$ for all positive integers $n$. Which of the following options are correct?\\
(1) If $a_{1} = 1$, then $a_{2} = 1$\\
(2) If $a_{1}$ is an integer, then every term of the sequence is an integer\\
(3) If $a_{1}$ is irrational, then every term of the sequence is irrational\\
(4) $a_{2} \leq a_{4} \leq \cdots \leq a_{2n} \leq \cdots$ (where $n$ is a positive integer)\\
(5) If $a_{k}$ is odd, then $a_{k+2}, a_{k+4}, \ldots, a_{k+2n}, \ldots$ are all odd (where $n$ is a positive integer)