收录高三寒假作业61新题

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wangweiye7840 2024-01-25 14:12:33 +08:00
parent 371c357303
commit 4dffb5ca89
2 changed files with 188 additions and 1 deletions

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20240125-140601
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"20230118\t王伟叶"
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@ -648682,6 +648684,188 @@
"space": "4em",
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"024091": {
"id": "024091",
"content": "等比数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 若 $a_3+4S_2=0$, 则公比 $q=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
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"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
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"remark": "",
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"024092": {
"id": "024092",
"content": "若等比数列 $\\{a_n\\}$ 的各项均为正数, $a_1+2 a_2=3$, $a_3^2=4 a_2a_6$, 则 $a_4=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
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"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
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"024093": {
"id": "024093",
"content": "在正项等比数列 $\\{a_n\\}$ 中, 已知 $a_1a_2a_3=4$, $a_4a_5a_6=12$, $a_{n-1}a_na_{n+1}=324$($n \\geq 2$, $n \\in \\mathbf{N}$), 则 $n=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
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"same": [],
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"024094": {
"id": "024094",
"content": "已知数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, $a_1=1$, $S_n=2 a_{n+1}$, 则 $S_n=$\\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": "",
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"024095": {
"id": "024095",
"content": "已知 $\\{a_n\\}$ 是递减的等比数列, 且 $a_2=2$,. $a_1+a_3=5$, 则 $\\{a_n\\}$ 的通项公式为 $a_1a_2+a_2a_3+\\cdots+a_na_{n+1}=$\\blank{50}($n \\in \\mathbf{N}$, $n \\geq 1$)",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
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"same": [],
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"remark": "",
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"024096": {
"id": "024096",
"content": "已知等比数列 $\\{a_n\\}$ 为严格减数列, 且 $a_5^2=a_{10}$, $2(a_n+a_{n+2})=5 a_{n+1}$, 则数列 $\\{a_n\\}$ 的通项公式 $a_n=$\\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": [
"012999"
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"024097": {
"id": "024097",
"content": "无穷等比数列 $\\{a_n\\}$ 的各项和为 $S$, 若数列 $\\{b_n\\}$ 满足 $b_n=a_{3 n-2}+a_{3 n-1}+a_{3 n}$, 则数列 $\\{b_n\\}$的各项和为\\bracket{20}.\n\\fourch{$S$}{$3S$}{$S^2$}{$S^3$}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
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"remark": "",
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"024098": {
"id": "024098",
"content": "设等比数列 $\\{a_n\\}$ 的公比为 $q$, 则下列结论中正确的是\\blank{50}.\\\\\n\\textcircled{1} 数列 $\\{a_na_{n+1}\\}$ 是公比为 $q^2$ 的等比数列;\\\\\n\\textcircled{2} 数列 $\\{a_n+a_{n+1}\\}$ 是公比为 $q$ 的等比数列;\\\\\n\\textcircled{3} 数列 $\\{a_n-a_{n+1}\\}$ 是公比为 $q$ 的等比数列;\\\\\n\\textcircled{4} 数列 $\\{\\dfrac{1}{a_n}\\}$ 是公比为 $\\dfrac{1}{q}$ 的等比数列.",
"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": []
},
"024099": {
"id": "024099",
"content": "已知数列 $\\{a_n\\}$ 的首项 $a_1>0$, $a_{n+1}=\\dfrac{3 a_n}{2 a_n+1}$($n \\in N$, $n \\geq 1$), 且 $a_1=\\dfrac{2}{3}$.\\\\\n(1) 求证: $\\{\\dfrac{1}{a_n}-1\\}$ 是等比数列, 并求出 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 求数列 $\\{\\dfrac{1}{a_n}\\}$ 的前 $n$ 项和 $T_n$.",
"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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",