For a natural number $p \geqq 2$, a sequence $\left\{ a _ { n } \right\}$ satisfies the following three conditions. Which of the following in are correct? [4 points] Conditions (가) $a _ { 1 } = 0$ (나) $a _ { k + 1 } = a _ { k } + 1 \quad ( 1 \leqq k \leqq p - 1 )$ (다) $a _ { k + p } = a _ { k } \quad ( k = 1,2,3 , \cdots )$ 〈Remarks〉 ㄱ. $a _ { 2 k } = 2 a _ { k }$ ㄴ. $a _ { 1 } + a _ { 2 } + \cdots + a _ { p } = \frac { p ( p - 1 ) } { 2 }$ ㄷ. $a _ { p } + a _ { 2 p } + \cdots + a _ { k p } = k ( p - 1 )$ (1) ㄱ (2) ㄴ (3) ㄷ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
For a natural number $p \geqq 2$, a sequence $\left\{ a _ { n } \right\}$ satisfies the following three conditions. Which of the following in <Remarks> are correct? [4 points]\\
\textbf{Conditions}\\
(가) $a _ { 1 } = 0$\\
(나) $a _ { k + 1 } = a _ { k } + 1 \quad ( 1 \leqq k \leqq p - 1 )$\\
(다) $a _ { k + p } = a _ { k } \quad ( k = 1,2,3 , \cdots )$\\
\textbf{〈Remarks〉}\\
ㄱ. $a _ { 2 k } = 2 a _ { k }$\\
ㄴ. $a _ { 1 } + a _ { 2 } + \cdots + a _ { p } = \frac { p ( p - 1 ) } { 2 }$\\
ㄷ. $a _ { p } + a _ { 2 p } + \cdots + a _ { k p } = k ( p - 1 )$\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ