From 6659deeee8185505287eb1766cec8617964b232c Mon Sep 17 00:00:00 2001
From: wangweiye7840 <kj_wangweiye@126.com>
Date: Thu, 25 Jan 2024 15:36:20 +0800
Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?=
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MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 工具v2/文本文件/新题收录列表.txt |   3 +
 题库0.3/Problems.json            | 267 ++++++++++++++++++++++++++++++-
 2 files changed, 265 insertions(+), 5 deletions(-)

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 41cc84aa..92df77d4 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
@@ -229,3 +229,6 @@
 20240125-153148
 024223:024238
 
+20240125-153606
+024239:024241,020797,024242:024250,004660
+
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index be455d49..7f089e86 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -57589,7 +57589,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024241"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -195757,7 +195759,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024241"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -361813,7 +361817,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024249"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -388843,7 +388849,9 @@
             "20230128\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024249"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -405212,7 +405220,9 @@
             "20230221\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024249"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -651806,6 +651816,253 @@
         "space": "4em",
         "unrelated": []
     },
+    "024239": {
+        "id": "024239",
+        "content": "在等差数列 $\\{a_n\\}$ 中, 若 $a_1, a_2, a_4$ 成等比数列, 其公比为 $q$, 则 $q=$\\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": []
+    },
+    "024240": {
+        "id": "024240",
+        "content": "等差数列 $\\{a_n\\}, a_1=\\dfrac{5}{6}$, 公差 $d=-\\dfrac{1}{6},\\{a_n\\}$ 的前 $n$ 项的和为 $S_n$. 若 $S_k=-5$, 则 $k=$\\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": []
+    },
+    "024241": {
+        "id": "024241",
+        "content": "等差数列前 $4$ 项和为 $124$, 最后 $4$ 项和为 $156$, 若它的各项和为 $210$, 则该数列的项数为\\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": [
+            "001767",
+            "006706"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024242": {
+        "id": "024242",
+        "content": "若 $\\alpha:(\\dfrac{1}{4})^x,(\\dfrac{1}{2})^x, 2^{x-4}$ 成等比数列; $\\beta: \\lg x, \\lg (x+2), \\lg (2 x+1)$ 成等差数列. 则 $\\alpha$ 是 $\\beta$ 的条件. (填入``充分不必要''、``必要不充分''、``充要''、``不充分不必要''之一)",
+        "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": []
+    },
+    "024243": {
+        "id": "024243",
+        "content": "已知\\textcircled{1}、\\textcircled{2}、\\textcircled{3}是三个陈述句, 其中\\\\\n\\textcircled{1}: 数列 $\\{a_n\\}$ 是等差数列, 且公差大于 $0$ ;\\\\\n\\textcircled{2}: 数列 $\\{a_n\\}$ 是等比数列, 且公比大于 $1$ ;\\\\\n\\textcircled{3}: 数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$, 且 $2S_n<S_{n-1}+S_{n+1}$($n \\geq 2$, $n \\in \\mathbf{N}$).\\\\\n则在\\textcircled{1}、\\textcircled{2}、\\textcircled{3}中, 能成为``数列 $\\{a_n\\}$ 是递增数列''的充分条件的陈述句的序号为\\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": []
+    },
+    "024244": {
+        "id": "024244",
+        "content": "一个公比为 $q$ 的无穷等比数列 $\\{a_n\\}$ 中, 若 $|q|<1$, 且有任意连续两项之和等于这两项后面所有项之和, 那么 $q=$\\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": []
+    },
+    "024245": {
+        "id": "024245",
+        "content": "某气象学院用 $3.2$ 万元买了一台天文观测仪, 已知这台观测仪从启用的第一天起连续使用, 第 $n$天的维修保养费为 $\\dfrac{n+49}{10}$ 元 ($n$ 是正整数) .使用它直至报废最合算(所谓报废最合算是指使用的这台仪器的平均耗资最少)为止, 一共使用了\\blank{50}天.",
+        "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": []
+    },
+    "024246": {
+        "id": "024246",
+        "content": "《尘劫记》 是在元代的《算学启蒙》和明代的《算法统宗》的基础上编撰的一部古典数学著作, 其中记载了一个这样的问题: 假设每对老鼠每月生子一次, 每月生 $12$ 只, 且雌雄各半. $1$ 个月后, 有一对老鼠生了 $12$ 只小老鼠, 一共有 $14$ 只; $2$ 个月后, 每对老鼠各生了 $12$ 只小老鼠, 一共有 $98$ 只.以此类推, 假设 $n$ 个月后共有老鼠 $a_n$ 只, 则 $a_{12}=$\\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": []
+    },
+    "024247": {
+        "id": "024247",
+        "content": "设 $p \\in \\mathbf{R}$. 数列 $\\{a_n\\}$ 是等比数列, $\\{a_n\\}$ 的前 $n$ 项和 $S_n=2^n+p$.\\\\\n(1) 求 $p$ 的值及数列 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 若数列 $\\{b_n\\}$ 满足 $b_n=\\log _2a_n$, 求数列 $\\{b_n\\}$ 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": []
+    },
+    "024248": {
+        "id": "024248",
+        "content": "数列 $\\{a_n\\}$ 的前 $n$ 项和 $S_n=\\dfrac{1}{2}n^2-2 n, n$ 是正整数, 数列 $\\{b_n\\}$ 满足 $b_n=\\dfrac{a_n+1}{a_n}, n$ 是正整数.\\\\\n(1) 判断数列 $\\{a_n\\}$ 是否为等差数列?并说明理由;\\\\\n(2) 求数列 $\\{b_n\\}$ 中值最大和值最小的项.",
+        "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": []
+    },
+    "024249": {
+        "id": "024249",
+        "content": "定义``等和数列'': 在一个数列中, 如果每一项与它的后一项的和都为同一个常数, 那么这个数列叫做等和数列, 这个常数叫做该数列的公和. 已知数列 $\\{a_n\\}$ 是等和数列, 且 $a_1=2$, 公和为 $5$.\\\\\n(1) 求数列 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 求数列 $\\{a_n\\}$ 的前 $n$ 项和 $S_n$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "012922",
+            "014558",
+            "013951"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "024250": {
+        "id": "024250",
+        "content": "某企业 $2019$ 年的纯利润为 $500$ 万元, 因设备老化等原因, 企业的生产能力将逐年下降, 若不进行技术改造, 预测从今年起每年比上一年纯利润减少 $20$ 万元, 今年初该企业一次性投人资金 $600$ 万元进行技术改造, 预测在未扣除技术改造资金的情况下, 第 $n$ 年(今年为第一年)的利润为 $500(1+\\dfrac{1}{2 n})$ 万元.\\\\\n(1) 设从今年起的前 $n$ 年, 若该企业不进行技术改造的累计纯利润为 $A_n$ 万元, 进行技术改造后的累计纯利润为 $B_n$ 万元(需扣除技术改造资金), 求 $A_n$ 与 $B_n$ 的表达式;\\\\\n(2) 依上述预测, 从今年起该企业至少经过多少年, 进行技术改造后的累计纯利润超过不进行技术改造的累计纯利润?",
+        "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.",