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职教组卷
  • 题型:解答题 题类:其他 难易度:较易

    已知数列\(\{a_{n}\}\)是等差数列,其前\(n\)项和为\(S_{n}\),数列\(\left\{ \left. b_{n} \right. \right\}\)是公比大于\(0\)的等比数列,且\(b_{1}=-2a_{1}=2\), \(a_{3}+b_{2}=-1\), \(S_{3}+2b_{3}=7\).

    \((1)\)求数列\(\{a_{n}\}\)和\(\left\{ \left. b_{n} \right. \right\}\)的通项公式;

    \((2)\)令\(c_{n}=\begin{cases} 2,n为奇数 \\ \dfrac{-2a_{n}}{b_{n}},n为偶数 \end{cases}\),求数列\(\left\{ \left. c_{n} \right. \right\}\)的前\(n\)项和\(T_{n}\).

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