共50条信息
已知等比数列\(\{a_{n}\}\)的公比\(q > 1\),\(a_{1}=1\),且\(2a_{2}\),\(a_{4}\),\(3a_{3}\)成等差数列.
\((1)\)求数列\(\{a_{n}\}\)的通项公式;
\((2)\)记\(b_{n}=2na_{n}\),求数列\(\{b_{n}\}\)的前\(n\)项和\(T_{n}\).
等比数列\(\{a_{n}\}\)中,已知\(a_{1}=2\),\(a_{4}=16\).
\((2)\)若\(a_{3}\),\(a_{5}\)分别为等差数列\(\{b_{n}\}\)第\(3\)项和第\(5\)项,求数列\(\{b_{n}\}\)的通项公式及前\(n\)项和\(S_{n}\).
在等比数列\(\{a_{n}\}\)中,已知\(a_{3}+a_{6}=36\),\(a_{4}+a_{7}=18\),\({{a}_{n}}=\dfrac{{1}}{{2}}\),求\(n\)的值.
设\(\left\{ {{a}_{n}} \right\}\)是公比为正数的等比数列,若\(a_{1}^{{}}=1,{{a}_{5}}=16\),则数列\(\left\{ {{a}_{n}} \right\}\)前\(7\)项的和为( )
已知等比数列\(\{\)\(a_{n}\)\(\}\)满足\(a\)\({\,\!}_{1}=3\),\(a\)\({\,\!}_{1}+\)\(a\)\({\,\!}_{3}+\)\(a\)\({\,\!}_{5}=21\),则\(a\)\({\,\!}_{3}+\)\(a\)\({\,\!}_{5}+\)\(a\)\({\,\!}_{7}=(\) \()\)
已知数列\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项之和为\({{S}_{n}}\)满足\({{S}_{n}}=2{{a}_{n}}-2\).
\((\)Ⅰ\()\)求数列\(\left\{ {{a}_{n}} \right\}\)的通项公式;
\((\)Ⅱ\()\)求数列\(\left\{ (2n-1)\cdot {{a}_{n}} \right\}\)的前\(n\)项和\({{T}_{n}}\).
已知等比数列\(\left\{ {{a}_{n}} \right\}\)满足\({{a}_{1}}+{{a}_{2}}=3,{{a}_{2}}+{{a}_{3}}=6\) ,则\({{a}_{7}}= (\) \()\)
设\({S}_{n} \) 是数列\(\{{a}_{n}\} \) 的前 \(n\) 项和,已知\({a}_{1}=3,{a}_{n+1}=2{S}_{n}+3 \).
\((1)\)求数列\(\{{a}_{n}\} \) 的通项公式;
\((2)\)令\({b}_{n}=(2n-1){a}_{n} \),求数列\(\{{b}_{n}\} \) 的前 \(n\) 项和\({T}_{n} \).
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