If \( a_{k} a_{k-1}+a_{k-1} a_{k-2}=2 a_{k} a_{k-2}, k \geq 3 \) an...

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If \( a_{k} a_{k-1}+a_{k-1} a_{k-2}=2 a_{k} a_{k-2}, k \geq 3 \) and \( a_{1}=1 \), here \( S_{p}=\sum_{k=1}^{p} \frac{1}{a_{k}} \) and given that \( \frac{S_{2 p}}{S_{p}} \) does not depend on p then \( \frac{1}{\mathrm{a}_{2016}} \) may be
P
(A) 4031
(B) 1
(C) 2016
(D) \( 2017 / 2 \)
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