如图，点列\(\{A_{n}\}\)，\(\{B_{n}\}\)分别在某锐角的两边上，且\(\left| {{A}_{n}}{{A}_{n+1}} ight|=\left| {{A}_{n+1}}{{A}_{n+2}} ight|,{{A}_{n}}e {{A}_{n+2}},n\in {{N}^{*}}\)，\(\left| {{B}_{n}}{{B}_{n+1}} ight|=\left| {{B}_{n+1}}{{B}_{n+2}} ight|,{{B}_{n}}e {{B}_{n+2}},n\in {{N}^{*}}\)，\((Peq Q \)表示点\(P\)与\(Q\)不重合\()\)，若\({d}_{n}=\left|{A}_{n}{B}_{n}ight| \)\(S_{n}\)为\(∆{A}_{n}{B}_{n}{B}

如图，点列\(\{A_{n}\}\)，\(\{B_{n}\}\)分别在某锐角的两边上，且\(\left| {{A}_{n}}{{A}_{n+1}} \right|=\left| {{A}_{n+1}}{{A}_{n+2}} \right|,{{A}_{n}}\ne {{A}_{n+2}},n\in {{N}^{*}}\)，\(\left| {{B}_{n}}{{B}_{n+1}} \right|=\left| {{B}_{n+1}}{{B}_{n+2}} \right|,{{B}_{n}}\ne {{B}_{n+2}},n\in {{N}^{*}}\)，\((P\neq Q \)表示点\(P\)与\(Q\)不重合\()\)，若\({d}_{n}=\left|{A}_{n}{B}_{n}\right| \) \(S_{n}\)为\(∆{A}_{n}{B}_{n}{B}_{n+1} \)的面积，则\((\) \()\)

A．\({ }\!\!\{\!\!{ }S_{n}^{{}}{ }\!\!\}\!\!{ }\)是等差数列

B．\({ }\!\!\{\!\!{ }S_{n}^{2}{ }\!\!\}\!\!{ }\)是等差数列

C．\({ }\!\!\{\!\!{ }d_{n}^{{}}{ }\!\!\}\!\!{ }\)是等差数列

D．\({ }\!\!\{\!\!{ }d_{n}^{2}{ }\!\!\}\!\!{ }\)是等差数列

【考点】等差数列的概念,相似三角形的判定及性质

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【解答】请登陆后查看

难度：较易

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