共50条信息
在等差数列\(\{{{a}_{n}}\}\)中,\({{a}_{2}}+{{a}_{7}}=-23\),\({{a}_{3}}+{{a}_{8}}=-29\).
\((1)\)求数列\(\{{{a}_{n}}\}\)的通项公式;
\((2)\)设数列\(\{{{a}_{n}}+{{b}_{n}}\}\)是首项为\(1\),公比为\(q\)的等比数列,求\(\{{{b}_{n}}\}\)的前\(n\)项和\({{S}_{n}}\).
在等比数列\(\left\{ {{a}_{n}} \right\}\)中,已知\({{a}_{4}}=8{{a}_{1}}\),且\({{a}_{1}},{{a}_{2}}+1,{{a}_{3}}\)成等差数列.
\((1)\)求数列\(\left\{ {{a}_{n}} \right\}\)的通项公式
\((2)\)求数列\(\left\{ \left| {{a}_{n}}-4 \right| \right\}\)的前\(n\)项和\({{S}_{n}}\).
等比数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),若\(a_{n} > 0\),\(q > 1\),\(a_{3}+a_{5}=20\),\(a_{2}a_{6}=64\),则\(S_{5}=\)________.
设数列\(\{a_{n}\}\)中, \(a_{1}=2\), \(a_{n+1}= \dfrac{2}{a_{n}+1}\), \(b_{n}=\left| \left. \dfrac{a_{n}+2}{a_{n}-1} \right. \right|\), \(n∈N^{*}\),则数列\(\left\{ \left. b_{n} \right. \right\}\)的通项公式为\(b_{n}=\)__________.
在各项均为正数的等比数列\(\{a_{n}\}\)中,\(a_{6}=3\),则\(a_{4}+a_{8}\)
数列\(\left\{ {{a}_{n}} \right\}\)是各项为正数的等比数列,且\({{a}_{4}}=2\),已知函数\(f(x)={\log }_{ \frac{1}{2}}x \),则\(f\left( a_{1}^{3} \right)+f\left( a_{2}^{3} \right)+\cdot \cdot \cdot +f\left( a_{7}^{3} \right)=\)( )
已知数列\(\{a_{n}\}\)为等比数列,\(a_{4}+a_{7}=2\),\(a_{⋅}a_{6}=-8\),则\(a_{1}+a_{10}\)的值为\((\) \()\)
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