记函数\(y={e}^{x} \)在\(x=n\left(n=1,2,3……ight) \)处的切线为\({l}_{n} .\) 若切线\({l}_{n} \)与\({l}_{n+1} \)的交点坐标为\(\left({A}_{n},{B}

记函数\(y={e}^{x} \)在\(x=n\left(n=1,2,3……\right) \)处的切线为\({l}_{n} .\) 若切线\({l}_{n} \)与\({l}_{n+1} \)的交点坐标为\(\left({A}_{n},{B}_{n}\right) \)，那么

A．数列\(\left\{{A}_{n}\right\} \)是等差数列，数列\(\left\{{B}_{n}\right\} \)是等比数列

B．数列\(\left\{{A}_{n}\right\} \)与\(\left\{{B}_{n}\right\} \)都是等差数列

C．数列\(\left\{{A}_{n}\right\} \)是等比数列，数列\(\left\{{B}_{n}\right\} \)是等差数列

D．数列\(\left\{{A}_{n}\right\} \)与\(\left\{{B}_{n}\right\} \)都是等比数列

【考点】利用导数研究曲线上某点切线方程,等差数列的通项公式,等比数列的通项公式,直线的点斜式方程

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难度：较易