添加三道关联题

题库0.3/Problems.json

@@ -550133,7 +550133,9 @@
             "20221231\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "022930"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -550199,7 +550201,9 @@
             "20221231\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "022931"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -550795,7 +550799,9 @@
             "20221231\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "022932"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -612223,6 +612229,82 @@
         "space": "",
         "unrelated": []
     },
+    "022930": {
+        "id": "022930",
+        "content": "已知等比数列$\\{a_n\\}$的前$5$项和为$10$, 前$10$项和为$60$, 则这个数列的前$15$项和是\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第四单元"
+        ],
+        "genre": "",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一校本作业选择性必修第四章-20231211修改",
+        "edit": [
+            "20221231\t王伟叶",
+            "20231211\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020755"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022931": {
+        "id": "022931",
+        "content": "已知$a$为常数, 求$a+a^3+a^5+\\cdots+a^{2 n+1}$.",
+        "objs": [],
+        "tags": [
+            "第四单元"
+        ],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一校本作业选择性必修第四章-20231211修改",
+        "edit": [
+            "20221231\t王伟叶",
+            "20231211\t王伟叶",
+            "20231211\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020758"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "022932": {
+        "id": "022932",
+        "content": "写出无穷数列$\\{a_n\\}$的一个通项公式, 使它的前$4$项分别是下列各数:\\\\\n(1) $4,8,12,16$: \\blank{50};\\\\\n(2) $\\dfrac 12, \\dfrac 23, \\dfrac 34, \\dfrac 45$: \\blank{50};\\\\\n(3) $-\\dfrac 1{2 \\times 1}, \\dfrac 1{2 \\times 2},-\\dfrac 1{2 \\times 3}, \\dfrac 1{2 \\times 4}$: \\blank{50};\\\\\n(4) $1,-\\sqrt[3]2, \\sqrt[3]3,-\\sqrt[3]4$: \\blank{50};\\\\\n(5) $\\dfrac{2}{3}, -\\dfrac{3}{8}, \\dfrac{4}{15}, -\\dfrac{5}{24}$: \\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第四单元"
+        ],
+        "genre": "",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一校本作业选择性必修第四章-20231211修改",
+        "edit": [
+            "20221231\t王伟叶",
+            "20231211\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020785"
+        ],
+        "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.",