Let \( x \) and \( y \) be real numbers such that \( x, x+2 y \) and \( 2 x+y \) are in \( A P \....

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Let \( x \) and \( y \) be real numbers such that \( x, x+2 y \) and \( 2 x+y \) are in \( A P \) and \( (y+1)^{2}, x y+5 \) and \( (x+1)^{2} \) are in \( G P \).
With this information, answer the following questions.
\( \mathrm{P} \)
The sum of four AM's between \( x \) and \( y \) and product of four GMs between \( x \) and \( y \) is
(1) \( 4+4 \sqrt{3} \)
(2) \( 4(2+\sqrt{3}) \)
(3) \( 8(1+\sqrt{3}) \)
(4) 17



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