添加一些自拟题目及一个关联题目

题库0.3/Problems.json

@@ -100180,7 +100180,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "022971"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -615217,6 +615219,134 @@
         "space": "4em",
         "unrelated": []
     },
+    "022966": {
+        "id": "022966",
+        "content": "已知数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n=5-2 n$, 则通项 $a_n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231225\t徐慧"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022967": {
+        "id": "022967",
+        "content": "已知各项均为正数的数列 $\\{a_n\\}$ 满足 $\\sqrt{a_1}+\\sqrt{a_2}+\\cdots+\\sqrt{a_n}=n^2+3 n$($n \\in \\mathbf{N}$ 且 $n \\geq 1$), 则 $\\dfrac{a_1}{2}+\\dfrac{a_2}{3}+\\cdots+ \\dfrac{a_n}{n+1}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231225\t徐慧"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022968": {
+        "id": "022968",
+        "content": "已知数列 $\\{x_n\\}$ 的通项公式为 $x_n=n a^n$, $n \\in \\mathbf{N}$ 且 $n \\geq 1$, 其中实数 $a>0$. 若数列 $\\{x_n\\}$ 是严格减数列, 则 $a$ 的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231225\t徐慧"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022969": {
+        "id": "022969",
+        "content": "设 $y=f(x)$ 是定义在正整数集上的函数, 且满足:``当 $f(k) \\geq k^2$ 成立时, 总可以推出 $f(k+1) \\geq(k+1)^2$ 成立'', 则当 $k \\in \\mathbf{N}$ 且 $k \\geq 1$ 时, 下列说法正确的是\\bracket{20}.\n\\onech{若 $f(2) \\geq 4$ 成立, 则当 $k \\geq 1$ 时, 均有 $f(k) \\geq k^2$ 成立}{若 $f(3) \\geq 9$ 成立, 则当 $k \\leq 3$ 时, 均有 $f(k) \\geq k^2$ 成立}{若 $f(4)=16$ 成立, 则当 $k \\geq 5$ 时, 均有 $f(k) \\geq k^2$ 成立}{若 $f(5)<25$ 成立, 则当 $k \\geq 6$ 时, 均有 $f(k)<k^2$ 成立}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231225\t徐慧"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022970": {
+        "id": "022970",
+        "content": "设数列 $\\{a_n\\}$, 下列正确的是\\bracket{20}.\n\\onech{若 $a_n^2=4^n$, $n \\in \\mathbf{N}$ 且 $n \\geq 1$, 则 $\\{a_n\\}$ 为等比数列}{若 $a_n \\cdot a_{n+2}=a_{n+1}^2$, $n \\in \\mathbf{N}$ 且 $n \\geq 1$, 则 $\\{a_n\\}$ 为等比数列}{若 $a_m \\cdot a_n=2^{m+n}, m$, $n \\in \\mathbf{N}$ 且 $n, m \\geq 1$, 则 $\\{a_n\\}$ 为等比数列}{若 $a_n \\cdot a_{n+3}=a_{n+1}\\cdot a_{n+2}$, $n \\in \\mathbf{N}$ 且 $n \\geq 1$, 则 $\\{a_n\\}$ 为等比数列}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231225\t徐慧"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022971": {
+        "id": "022971",
+        "content": "已知数列$\\{a_n\\}$满足: $a_n=\\dfrac 1{n-5.5}$, 则此数列中最大项的值为\\blank{50}.",
+        "objs": [
+            "K0406005X"
+        ],
+        "tags": [
+            "第四单元",
+            "2023届高三-第一轮复习讲义-31-数列的递推与通项及数学归纳法"
+        ],
+        "genre": "",
+        "ans": "$2$, $-2$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20231225修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20231225\t朱敏慧"
+        ],
+        "same": [],
+        "related": [
+            "003215"
+        ],
+        "remark": "",
+        "space": "",
+        "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.",