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收录高三寒假作业59新题

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wangweiye7840 2024-01-25 14:03:15 +08:00
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3
工具v2/文本文件/新题收录列表.txt
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@ -175,3 +175,6 @@
20240125-135948
020205,017574,024067:024068,013656,024069:024072
20240125-140305
024073:024081

201
题库0.3/Problems.json
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@ -14446,7 +14446,8 @@
],
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"023496",
"024081"
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@ -301311,7 +301312,8 @@
],
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@ -449717,7 +449719,9 @@
"20230503\t王伟叶"
],
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"024073"
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@ -492947,7 +492951,9 @@
"20230704\t王伟叶"
],
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"space": "4em",
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@ -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"
],
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"related": [
"000403",
"010778"
],
"remark": "",
"space": "4em",
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},
"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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",