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 7b86fb87..1a1491b2 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 @@ -178,3 +178,6 @@ 20240125-140305 024073:024081 +20240125-140601 +024082:024090 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index ca518efe..cc067594 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -648502,6 +648502,186 @@ "space": "4em", "unrelated": [] }, + "024082": { + "id": "024082", + "content": "若在等差数列 $\\{a_n\\}$ 中, $a_4+a_8=10$, $a_{10}=6$, 则公差 $d=$\\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": [] + }, + "024083": { + "id": "024083", + "content": "在等差数列 $\\{a_n\\}$ 中, 若 $S_n$ 为 $\\{a_n\\}$ 的前 $n$ 项和, $2 a_7=a_8+5$, 则 $S_{11}$ 的值是\\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": [] + }, + "024084": { + "id": "024084", + "content": "设等差数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 若 $a_m=4$, $S_m=0$, $S_{m+2}=14,$($m \\geq 2$, $m \\in \\mathbf{N}$), 则 $a_{2023}$的值为\\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": [] + }, + "024085": { + "id": "024085", + "content": "已知等差数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 若 $S_7=a_4$, 则以下结论中正确的是\\blank{50}.(填序号)\\\\\n\\textcircled{1} $a_1+a_3=0$; \\textcircled{2} $a_3+a_5=0$; \\textcircled{3} $S_3=S_4$; \\textcircled{4} $S_4=S_5$.", + "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": [] + }, + "024086": { + "id": "024086", + "content": "等差数列 $\\{a_n\\}$ 中, 若 $S_n$ 是其前 $n$ 项和, $a_1=-9$, $\\dfrac{S_9}{9}-\\dfrac{S_7}{7}=2$, 则 $a_n=$\\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": [] + }, + "024087": { + "id": "024087", + "content": "等差数列 $\\{a_n\\}$ 的各项均不为零, 其前 $n$ 项和为 $S_n$. 若 $a_{n+1}^2=a_{n+2}+a_n$, 则 $S_{2 n+1}=$\\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": [] + }, + "024088": { + "id": "024088", + "content": "已知 $S_n$ 是等差数列 $\\{a_n\\}$ 的前 $n$ 项和, 且 $S_6>S_7>S_5$, 给出下列五个命题: \\textcircled{1} $d<0$; \\textcircled{2} $S_{11}>0$; \\textcircled{3} $S_{12}>0$; \\textcircled{4} 数列 $\\{S_n\\}$ 中的最大项为 $S_{11}$; \\textcircled{5} $|a_6|>|a_7|$, 其中正确命题的个数为\\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": [] + }, + "024089": { + "id": "024089", + "content": "已知数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 若 $a_1=1$, $a_n+a_{n+1}=2 n+1$($n \\in \\mathbf{N}$, $n \\geq 1$), 则 $S_{21}$ 的值为\\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": [] + }, + "024090": { + "id": "024090", + "content": "记 $S_n$ 为等差数列 $\\{a_n\\}$ 的前 $n$ 项和. 已知 $S_9=-a_5$.\\\\\n(1) 若 $a_3=4$, 求 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 若 $a_1>0$, 求使得 $S_n\\geq a_n$ 的 $n$ 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": [], + "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