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            • 1.
              已知数列\(\{a_{n})\)的通项公式为\(a_{n}= \dfrac {1+(-1)^{n+1}}{2}\),则该数列的前\(4\)项依次为\((\)  \()\)
              A.\(1\),\(0\),\(1\),\(0\)
              B.\(0\),\(1\),\(0\),\(1\)
              C.\( \dfrac {1}{2},0, \dfrac {1}{2},0\)
              D.\(2\),\(0\),\(2\),\(0\)
            • 2. 在数列\( \dfrac { \sqrt {5}}{3}, \dfrac { \sqrt {10}}{8}, \dfrac { \sqrt {17}}{a+b}, \dfrac { \sqrt {a-b}}{24}, \dfrac { \sqrt {37}}{35},…\)中,则实数\(a=\) ______ ,\(b=\) ______ .
            • 3. 数列\( \dfrac {2}{3}\),\( \dfrac {4}{5}\),\( \dfrac {8}{7}\),\( \dfrac {16}{9}\),\(…\)的一个通项公式是 ______ .
            • 4.

              若数列\(\{a_{n}\}\)的通项满足\( \dfrac{a_{n}}{n}=n-2\),那么\(15\)是这个数列的第________项.

            • 5. 数列\( \dfrac {1}{3}\),\( \dfrac {1}{8}\),\( \dfrac {1}{15}\),\( \dfrac {1}{24}\),\(…\)的一个通项公式为\((\)  \()\)
              A.\(a_{n}= \dfrac {1}{2^{n}+1}\)
              B.\(a_{n}= \dfrac {1}{n+2}\)
              C.\(a_{n}= \dfrac {1}{n(n+2)}\)
              D.\(a_{n}= \dfrac {1}{2^{n}-1}\)
            • 6.
              数列\(6\),\(9\),\(14\),\(21\),\(30\),\(…\)的一个通项公式是\((\)  \()\)
              A.\(3n+3\)
              B.\(2n^{2}+1\)
              C.\(2^{n}+n+3\)
              D.\(n^{2}+5\)
            • 7. 数列\(-1\),\(1\),\(- \dfrac {9}{5}\),\( \dfrac {27}{7}\),\(…\)的一个通项公式为 ______
            • 8. 设数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),若\(S_{2}=4\),\(a_{n+1}=2S_{n}+1\),\(n∈N^{*}\),则\(a_{1}=\)______,\(S_{5}=\)______.
            • 9.

              数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\),若数列\(\{a_{n}\}\)的各项按如下规律排列:\( \dfrac{1}{2}\),\( \dfrac{1}{3}\),\( \dfrac{2}{3}\),\( \dfrac{1}{4}\),\( \dfrac{2}{4}\),\( \dfrac{3}{4}\),\( \dfrac{1}{5}\),\( \dfrac{2}{5}\),\( \dfrac{3}{5}\),\( \dfrac{4}{5}\),\(…\),\( \dfrac{1}{n}\),\( \dfrac{2}{n}\),\(…\),\( \dfrac{n-1}{n}\),\(…\),有如下运算和结论:其中正确的结论有________\(.(\)将你认为正确的结论序号都填上\()\)

              \(①a_{24}= \dfrac{3}{8}\);

              \(②\)数列\(a_{1}\),\(a_{2}+a_{3}\),\(a_{4}+a_{5}+a_{6}\),\(a_{7}+a_{8}+a_{9}+a_{10}\),\(…\)是等比数列;

              \(③\)数列\(a_{1}\),\(a_{2}+a_{3}\),\(a_{4}+a_{5}+a_{6}\),\(a_{7}+a_{8}+a_{9}+a_{10}\),\(…\)的前\(n\)项和为\(T_{n}= \dfrac{n^{2}+n}{4}\);

              \(④\)若存在正整数\(k\),使\({S}_{k} < 10,{S}_{k+1}\geqslant 10 \),则\({a}_{k}= \dfrac{5}{7} \).

            • 10. 在数列\({\) \(a_{n}\)\(}\)中,若 \(a\)\({\,\!}_{1}=2\),且对任意的正整数 \(p\)\(q\)都有 \(a_{p}\)\(q\)\(=\) \(a_{p}a_{q}\),则 \(a\)\({\,\!}_{8}\)的值为____.
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