A total of \( n \) arithmetic means are inserted between \( x \) and \( 2 y \) and further \( n ....

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A total of \( n \) arithmetic means are inserted between \( x \) and \( 2 y \) and further \( n \) arithmetic means are inserted
\( \mathrm{P} \)
between \( 2 x \) and \( y \). If the \( k^{\text {th }} \) arithmetic means of both sets are equal, then a relation between \( x \) and \( y \) is
(1) \( k y=(n-k) x \)
(2) \( k y=(n+1-k) x \)
(3) \( k(y+1)=(n-k) x \)
(4) \( k(y+1)=(n-1-k) x \)


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