设等差数列\( \left\{{a}_{n}\right\}\)的公差为\(d\)，若数列\( \left\{{a}_{1}{a}

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设等差数列\( \left\{{a}_{n}\right\}\)的公差为\(d\)，若数列\( \left\{{a}_{1}{a}_{n}\right\}\)为递减数列，则（）

A.\( d<0\)

B.\( d>0\)

C.\( {a}_{1}d>0\)

D.\( {a}_{1}d<0\)

参考答案：D

解析：

依题意，数列\( \left\{{a}_{n}\right\}\)是公差为\(d\)的等差数列，数列\( \left\{{a}_{1}{a}_{n}\right\}\)为递减数列，

所以\( {a}_{1}{a}_{n}>{a}_{1}{a}_{n+1}\)，\( {a}_{1}{a}_{n}>{a}_{1}\left({a}_{n}+d\right)\)，\( {a}_{1}{a}_{n}>{a}_{1}{a}_{n}+{a}_{1}d,{a}_{1}d<0\).

故选：D