csat-suneung· South-Korea· csat__math-science4 marks
In the coordinate plane, for a natural number $n$, let $A _ { n }$ be a square with vertices at the four points $$\left( n ^ { 2 } , n ^ { 2 } \right) , \left( 4 n ^ { 2 } , n ^ { 2 } \right) , \left( 4 n ^ { 2 } , 4 n ^ { 2 } \right) , \left( n ^ { 2 } , 4 n ^ { 2 } \right)$$ Let $a _ { n }$ be the number of natural numbers $k$ such that the square $A _ { n }$ and the graph of the function $y = k \sqrt { x }$ intersect. Which of the following statements in are correct? [4 points] Remarks ㄱ. $a _ { 5 } = 15$ ㄴ. $a _ { n + 2 } - a _ { n } = 7$ ㄷ. $\sum _ { k = 1 } ^ { 10 } a _ { k } = 200$ (1) ㄴ (2) ㄷ (3) ㄱ, ㄴ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
In the coordinate plane, for a natural number $n$, let $A _ { n }$ be a square with vertices at the four points
$$\left( n ^ { 2 } , n ^ { 2 } \right) , \left( 4 n ^ { 2 } , n ^ { 2 } \right) , \left( 4 n ^ { 2 } , 4 n ^ { 2 } \right) , \left( n ^ { 2 } , 4 n ^ { 2 } \right)$$
Let $a _ { n }$ be the number of natural numbers $k$ such that the square $A _ { n }$ and the graph of the function $y = k \sqrt { x }$ intersect. Which of the following statements in <Remarks> are correct? [4 points]
\textbf{Remarks}\\
ㄱ. $a _ { 5 } = 15$\\
ㄴ. $a _ { n + 2 } - a _ { n } = 7$\\
ㄷ. $\sum _ { k = 1 } ^ { 10 } a _ { k } = 200$\\
(1) ㄴ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ