已知\(\{a_{n}\}\)为等差数列，前\(n\)项和为\(S_{n}(n∈N^{*})\)，\(\{b_{n}\}\)是首项为\(2\)的等比数列，且公比大于\(0\)，\(b_{2}+b_{3}=12\)，\(b_{3}=a_{4}-2a_{1}\)，\(S_{11}=11b_{4}\)． \((\)Ⅰ\()\)求\(\{a_{n}\}\)和\(\{b_{n}\}\)的通项公式； \((\)Ⅱ\()\)求数列\(\{a_{2n}b_{n}\}\)的前\(n\)项和\((n∈N^{*}).\) --优优班--学霸训练营

已知\(\{a_{n}\}\)为等差数列，前\(n\)项和为\(S_{n}(n∈N^{*})\)，\(\{b_{n}\}\)是首项为\(2\)的等比数列，且公比大于\(0\)，\(b_{2}+b_{3}=12\)，\(b_{3}=a_{4}-2a_{1}\)，\(S_{11}=11b_{4}\)．
\((\)Ⅰ\()\)求\(\{a_{n}\}\)和\(\{b_{n}\}\)的通项公式；
\((\)Ⅱ\()\)求数列\(\{a_{2n}b_{n}\}\)的前\(n\)项和\((n∈N^{*}).\)

【考点】等差数列与等比数列的综合应用

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难度：较难

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