diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index a85e61f0..7b86fb87 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -175,3 +175,6 @@ 20240125-135948 020205,017574,024067:024068,013656,024069:024072 +20240125-140305 +024073:024081 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 80cbcc35..ca518efe 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -14446,7 +14446,8 @@ ], "same": [], "related": [ - "023496" + "023496", + "024081" ], "remark": "", "space": "", @@ -301311,7 +301312,8 @@ ], "same": [], "related": [ - "023496" + "023496", + "024081" ], "remark": "", "space": "4em", @@ -449717,7 +449719,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024073" + ], "remark": "", "space": "", "unrelated": [] @@ -492947,7 +492951,9 @@ "20230704\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024077" + ], "remark": "", "space": "4em", "unrelated": [] @@ -648309,6 +648315,193 @@ "space": "4em", "unrelated": [] }, + "024073": { + "id": "024073", + "content": "已知数列 $\\{a_n\\}$ 满足 $a_n=4 a_{n-1}+3$($n \\geq 2$, $n \\in \\mathbf{N}$), 若 $a_1=0$, 则 $a_5=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "016360" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024074": { + "id": "024074", + "content": "若数列 $\\{a_n\\}$ 的前 $n$ 项和 $S_n=n^2+3 n$, 则 $\\dfrac{a_4+a_5+a_6}{a_1+a_2+a_3}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024075": { + "id": "024075", + "content": "已知数列 $\\{a_n\\}$ 的前四项分别 $1,0,1,0$, 给出下列各式:\\\\\n\\textcircled{1} $a_n=\\dfrac{1}{2}[1+(-1)^{n+1}]$; \\textcircled{2} $a_n=\\sin ^2\\dfrac{n \\pi}{2}$; \\textcircled{3} $a_n=\\dfrac{1}{2}[1+(-1)^{n+1}]+(n-1)(n-2)$; \\textcircled{4} $a_n=\\begin{cases}0,& n=2 k,\\\\1,& n=2 k-1,\\end{cases}$($n \\geq 1$, $n \\in \\mathbf{N}$).\\\\\n其中可作为数列 $\\{a_n\\}$ 的通项公式的是\\blank{50}(填序号).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024076": { + "id": "024076", + "content": "在数列 $\\{a_n\\}$ 中, 若 $a_1=2$, $a_{n+1}=\\dfrac{1}{a_n}$, 则数列 $\\{a_n\\}$ 的通项 $a_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024077": { + "id": "024077", + "content": "记 $S_n$ 为数列 $\\{a_n\\}$ 的前 $n$ 项和.``任意正整数 $n$, 均有 $a_n>0$''是``$\\{S_n\\}$ 是严格增数列''的\\blank{50}条件.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "018289" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024078": { + "id": "024078", + "content": "已知数列 $\\{a_n\\}$ 中, $a_{n+1}=\\dfrac{a_n^2}{2 a_n-5}$, 若该数列既是等差数列又是等比数列, 则该数列前 $20$ 项和为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024079": { + "id": "024079", + "content": "已知数列 $\\{a_n\\}$ 的通项公式为 $a_n=\\dfrac{9^n(n+1)}{10^n},$($n \\geq 1$, $n \\in \\mathbf{N}$), 则数列 $\\{a_n\\}$ 的最大项是第\\blank{50}项.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024080": { + "id": "024080", + "content": "已知 $a_n=\\dfrac{n}{n^2+156},$($n \\geq 1$, $n \\in \\mathbf{N}$) 则数列 $\\{a_n\\}$ 的最大项是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024081": { + "id": "024081", + "content": "已知数列 $\\{a_n\\}$ 的通项公式是 $a_n=n^2+k n+4$. 若数列 $\\{a_n\\}$ 为严格增数列, 求实数 $k$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "000403", + "010778" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0