共50条信息
已知等比数列\(\left\{ \mathbf{a}_{\mathbf{n}} \right\}\)的公比\(\mathbf{q}{ > }0\),其前\(\mathbf{n}\)项和为\(\mathbf{S}_{\mathbf{n}}\),若\(\mathbf{a}_{\mathbf{1}}\mathbf{{=}1}\),\(\mathbf{4}\mathbf{a}_{\mathbf{3}}\mathbf{{=}}\mathbf{a}_{\mathbf{2}}\mathbf{a}_{\mathbf{4}}\).
\((1)\)求公比\(\mathbf{q}\)和\(\mathbf{a}_{\mathbf{5}}\)的值;
\((2)\)求证:\(\dfrac{\mathbf{S}_{\mathbf{n}}}{\mathbf{a}_{\mathbf{n}}}\mathbf{{ < }}2\).
设数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),若\(2\),\(S_{n}\),\(3a_{n}\)成等差数列,则\(S_{5}\)的值是\((\) \()\)
设等比数列\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项和\({{S}_{n}}\),已知\({{a}_{1}}{{a}_{2}}{{a}_{3}}=8\),\({{S}_{2n}}=3\left( {{a}_{1}}+{{a}_{3}}+ \right.\left. {{a}_{5}}+\cdots {{a}_{2n-1}} \right)\).
\((\)Ⅰ\()\)求数列\(\left\{ {{a}_{n}} \right\}\)的通项公式;
\((\)Ⅱ\()\)设\({{b}_{n}}=n{{S}_{n}}\),求数列\(\left\{ {{b}_{n}} \right\}\)的前\(n\)项和\({{T}_{n}}\).
已知正项等比数列\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项和为\({{S}_{n}}\),且\({{a}_{1}}{{a}_{6}}=2{{a}_{3}}\),\({{a}_{4}}\)与\({{a}_{6}}\)的等差中项为\(5\),则\({{S}_{5}}=\)( )
公差不为零的等差数列\(\{{{a}_{n}}\}\)中,\({{a}_{3}}=7\),又\({{a}_{2}},{{a}_{4}},{{a}_{9}}\)成等比数列.
\((1)\)求数列\(\{{{a}_{n}}\}\)的通项公式.
\((2)\)设\({{b}_{n}}={{2}^{{{a}_{n}}}}\),求数列\(\{{{b}_{n}}\}\)的前\(n\)项和\({{S}_{n}}\).
\(.\)在等比数列\(\{an\}\)中,若\({a}_{1}= \dfrac{1}{2} \),\(a_{4}=-4\),则\(|{a}_{1}|+|{a}_{2}|+⋯|{a}_{n}|= \)________.
已知等比数列\(\{{{a}_{n}}\}\)的前\(n\)项和记为\({{S}_{n}},\) \(a\)\({\,\!}_{3}=3\) , \(a\)\({\,\!}_{10}=384\).求该数列的公比\(q\)和通项公式\(S\)\({\,\!}_{n}\)
在等比数列\(\;\{\;{a}_{n}\;\}\; \)中,已知\({{a}_{1}}=1,\dfrac{{{a}_{5}}+{{a}_{7}}}{{{a}_{2}}+{{a}_{4}}}=\dfrac{1}{8}\),则\({{S}_{5}}\)的值为( )
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