添加关联题

题库0.3/Problems.json

@@ -603359,7 +603359,9 @@
             "20230905\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "022941"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -613404,6 +613406,29 @@
         "space": "",
         "unrelated": []
     },
+    "022941": {
+        "id": "022941",
+        "content": "设 $k \\in \\mathbf{R}$, 数列 $\\{a_n\\}$ 满足 $a_n=2 n+k$, 数列 $\\{b_n\\}$ 的通项公式为 $b_n=3^n$.\\\\\n(1) 若 $k=-113$, 设 $c_n=\\dfrac{a_n}{b_n}$, 求数列 $\\{c_n\\}$ 最大项及相应的序数;\\\\\n(2) 若 $k=1$, 设 $d_n=\\begin{cases}a_n,&  n \\text{为奇数}, \\\\b_n,&  n \\text{为偶数}.\\end{cases}$ 求数列 $\\{d_n\\}$ 的前 $n$ 项和 $S_n$.",
+        "objs": [],
+        "tags": [],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期周末卷19-20231218修改",
+        "edit": [
+            "20230905\t王伟叶",
+            "20231218\t朱敏慧"
+        ],
+        "same": [],
+        "related": [
+            "022591"
+        ],
+        "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.",