{"id":11936,"date":"2022-12-28T12:59:47","date_gmt":"2022-12-28T03:59:47","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11936"},"modified":"2023-01-03T11:34:21","modified_gmt":"2023-01-03T02:34:21","slug":"sequence-2","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/sequence-2.html","title":{"rendered":"\u7b49\u6bd4\u6570\u5217\uff1a\u516c\u5f0f\u3084\u7b49\u6bd4\u4e2d\u9805\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u3001\u5bfe\u6570\u306e\u8a08\u7b97"},"content":{"rendered":"\n<p>\u6570\u5217\u3067\u5b66\u3076\u57fa\u672c\u7684\u306a\u5185\u5bb9\u306b\u7b49\u6bd4\u6570\u5217\u304c\u3042\u308a\u307e\u3059\u3002\u7b49\u5dee\u6570\u5217\u3092\u5b66\u3093\u3060\u3042\u3068\u3001\u7b49\u6bd4\u6570\u5217\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u7279\u5b9a\u306e\u5024\u3092\u304b\u3051\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u6570\u5217\u304c\u7b49\u6bd4\u6570\u5217\u3067\u3059\u3002\u7b49\u6bd4\u6570\u5217\u306f\u91d1\u5229\u8a08\u7b97\u3067\u5229\u7528\u3055\u308c\u308b\u306a\u3069\u3001\u79c1\u305f\u3061\u306e\u751f\u6d3b\u3067\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u308b\u5206\u91ce\u3067\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u3092\u5f97\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u7b49\u6bd4\u4e2d\u9805\u3084\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306b\u95a2\u3059\u308b\u516c\u5f0f\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u307e\u305f\u3001\u7b49\u5dee\u6570\u5217\u3068\u7b49\u6bd4\u6570\u5217\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u308a\u3001\u7b49\u6bd4\u6570\u5217\u3068\u5bfe\u6570\u3092\u5229\u7528\u3059\u308b\u554f\u984c\u3092\u89e3\u3044\u305f\u308a\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u7b49\u6bd4\u6570\u5217\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7b49\u6bd4\u6570\u5217\u3092\u7528\u3044\u3066\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u3092\u51fa\u3059\u516c\u5f0f<\/h2>\n<p>\u7279\u5b9a\u306e\u5024\u3092\u304b\u3051\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u6570\u5217\u3092\u7b49\u6bd4\u6570\u5217\u3068\u3044\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u521d\u9805\u304c2\u3001\u516c\u6bd4\u304c3\u306e\u5834\u5408\u3001\u7b49\u6bd4\u6570\u5217\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/ofjv2.jpg\" alt=\"\" width=\"454\" height=\"109\" class=\"aligncenter size-full wp-image-11937\" \/><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u306f\u3069\u3046\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u307b\u3069\u306e\u4f8b\u3067\u3042\u308c\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8003\u3048\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/ofjv3.jpg\" alt=\"\" width=\"600\" height=\"102\" class=\"aligncenter size-full wp-image-11938\" 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loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/ofjv4.jpg\" alt=\"\" width=\"444\" height=\"109\" class=\"aligncenter size-full wp-image-11939\" \/><\/p>\n<p>\u3053\u306e\u3068\u304d\u3001\u771f\u3093\u4e2d\u306e\u6570\\(a\\)\u3092<span style=\"color: #ff0000;\">\u7b49\u6bd4\u4e2d\u9805<\/span>\u3068\u3044\u3044\u307e\u3059\u3002\u306a\u304a\u4e0a\u56f3\u3088\u308a\u3001\u7b49\u6bd4\u6570\u5217\u304c\\(a,b,c\\)\u306e\u9806\u3067\u4e26\u3093\u3067\u3044\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(b^2=ac\\)<\/li>\n<\/ul>\n<p>\u3053\u308c\u304c\u7b49\u6bd4\u4e2d\u9805\u3067\u91cd\u8981\u306a\u6027\u8cea\u3067\u3059\u3002\u771f\u3093\u4e2d\u306e\u6570\u304c\u308f\u304b\u3089\u306a\u304f\u3066\u3082\u3001\u4e21\u96a3\u306e\u6570\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u7b49\u6bd4\u4e2d\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(a,b,c\\)\u306f\u3053\u306e\u9806\u756a\u3067\u7b49\u6bd4\u6570\u5217\u3067\u3059\u3002\\(a,b,c\\)\u306e\u548c\u304c14\u3001\u7a4d\u304c64\u306e\u3068\u304d\u3001\\(a,b,c\\)\u306e\u5024\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u554f\u984c\u306e\u6761\u4ef6\u3088\u308a\u3001\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a+b+c=14\\)<\/li>\n<li>\\(abc=64\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\u3001\u7b49\u6bd4\u4e2d\u9805\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(b^2=ac\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\\(b^2=ac\\)\u3092\\(abc=64\\)\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001\\(b^3=64\\)\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(b=4\\)\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u3053\u3067\\(b=4\\)\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a=10-c\\)<\/li>\n<li>\\(ac=16\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\\(a=10-c\\)\u3092\\(ac=16\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(ac=16\\)<\/p>\n<p>\\((10-c)c=16\\)<\/p>\n<p>\\(-c^2+10c=16\\)<\/p>\n<p>\\(c^2-10c+16=0\\)<\/p>\n<p>\\((c-2)(c-8)=0\\)<\/p>\n<p>\\(c=2,8\\)<\/p>\n<p>\\(c=2\\)\u306e\u3068\u304d\u3001\\(a=8\\)\u3067\u3059\u3002\u307e\u305f\\(c=8\\)\u306e\u3068\u304d\u3001\\(a=2\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(2,4,8\\)\u3068\\(8,4,2\\)\u304c\u7b54\u3048\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u5c0e\u51fa\u3059\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u899a\u3048\u307e\u3057\u3087\u3046\u3002\u7b49\u5dee\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3068\u540c\u69d8\u306b\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u306f\u899a\u3048\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u7b49\u6bd4\u6570\u5217\u3067\u306f2\u30d1\u30bf\u30fc\u30f3\u306b\u5206\u3051\u3066\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u521d\u9805\\(a\\)\u3001\u516c\u6bd4\\(r\\)\u3001\u9805\u6570\\(n\\)\u3067\u3042\u308b\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306b\u3064\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\\(r=1\\)\u306e\u5834\u5408<\/strong><\/p>\n<p>\u516c\u6bd4\u304c1\u306e\u5834\u5408\u3001\u521d\u9805\\(a\\)\u304c\\(n\\)\u500b\u4e26\u3076\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u516c\u6bd4\u6570\u5217\u306e\u548c\\(S_n\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(S_n=an\\)<\/li>\n<\/ul>\n<p>\u521d\u9805\u3068\u9805\u6570\u3092\u304b\u3051\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u548c\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\\(r\u22601\\)\u306e\u5834\u5408<\/strong><\/p>\n<p>\u591a\u304f\u306e\u5834\u5408\u3001\u516c\u6bd4\u306f1\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\\(r\u22601\\)\u306e\u3068\u304d\u306b\u3064\u3044\u3066\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u5f97\u308b\u3068\u304d\u30012\u3064\u306e\u7b49\u6bd4\u6570\u5217\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u7b49\u6bd4\u6570\u5217\u306b\u5bfe\u3057\u3066\\(r\\)\u3092\u304b\u3051\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f15\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/djeh2.jpg\" alt=\"\" width=\"700\" height=\"131\" class=\"aligncenter size-full wp-image-11995\" \/><\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\((1-r)S_n=a-ar^n\\)<\/p>\n<p>\\((1-r)S_n=a(1-r^n)\\)<\/p>\n<p>\\(S_n=\\displaystyle\\frac{a(1-r^n)}{1-r}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u306a\u304a\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306b\\(-1\\)\u3092\u304b\u3051\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u304c\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(S_n=\\displaystyle\\frac{a(1-r^n)}{1-r}\\)\\(=\\displaystyle\\frac{a(r^n-1)}{r-1}\\)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u7b2c3\u9805\u304c\\(12\\)\uff0c\u7b2c4\u9805\u304c\\(-24\\)\u3067\u3042\u308b\u7b49\u6bd4\u6570\u5217\u306b\u3064\u3044\u3066\u3001\u7b2c5\u9805\u304b\u3089\u7b2c8\u9805\u307e\u3067\u306e\u548c\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\\(a_n=ar^{n-1}\\)\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_3=ar^2=12\\)<\/li>\n<li>\\(a_4=ar^3=-24\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\\(ar^2=12\\)\u3092\\(ar^3=-24\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(ar^3=-24\\)<\/p>\n<p>\\(12r=-24\\)<\/p>\n<p>\\(r=-2\\)<\/p>\n<p>\\(r=-2\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(a=3\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4e00\u822c\u9805\u306f\\(a_n=3\u00b7(-2)^{n-1}\\)\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u3057\u3066\u7b49\u5dee\u6570\u5217\u306e\u548c\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7b2c8\u9805\u307e\u3067\u306e\u548c\u304b\u3089\u3001\u7b2c4\u9805\u307e\u3067\u306e\u548c\u3092\u5f15\u3051\u3070\u3001\u7b2c5\u9805\u304b\u3089\u7b2c8\u9805\u306e\u548c\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u305d\u308c\u305e\u308c\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\u7b2c4\u9805\u307e\u3067\u306e\u548c<\/strong><\/p>\n<p>\\(S_4=\\displaystyle\\frac{3\\{1-(-2)^4\\}}{1-(-2)}\\)<\/p>\n<p>\\(S_4=1-16\\)<\/p>\n<p>\\(S_4=-15\\)<\/p>\n<p><strong>\u30fb\u7b2c8\u9805\u307e\u3067\u306e\u548c<\/strong><\/p>\n<p>\\(S_8=\\displaystyle\\frac{3\\{1-(-2)^8\\}}{1-(-2)}\\)<\/p>\n<p>\\(S_8=1-256\\)<\/p>\n<p>\\(S_8=-255\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(S_8-S_4=-255-(-15)=-240\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u306f\\(-240\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h2>\u7b49\u5dee\u6570\u5217\u3068\u7b49\u6bd4\u6570\u5217\u3092\u5229\u7528\u3059\u308b\u8a08\u7b97\u554f\u984c<\/h2>\n<p>\u7b49\u6bd4\u6570\u5217\u306e\u57fa\u672c\u3092\u5b66\u3093\u3060\u3089\u3001\u5fdc\u7528\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u7b49\u5dee\u6570\u5217\u3068\u7b49\u6bd4\u6570\u5217\u306e\u4e21\u65b9\u304c\u95a2\u308f\u308b\u554f\u984c\u306f\u5fdc\u7528\u554f\u984c\u3067\u51fa\u984c\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u6570\u5217\\(\\{a_n\\}\\)\u306f\u516c\u6bd4\u304c\u8ca0\u3067\u3042\u308b\u521d\u98051\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3059\u3002\u307e\u305f\u3001\u6570\u4f8b\\(\\{b_n\\}\\)\u306f\\(b_1\uff1da_3\\)\u3001\\(b_2\uff1da_4\\)\u3001\\(b_3\uff1da_2\\)\u3092\u6e80\u305f\u3059\u7b49\u5dee\u6570\u5217\u3067\u3059\u3002\u6570\u5217\\(\\{a_n\\}\\)\u3068\u6570\u5217\\(\\{b_n\\}\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\\(\\{a_n\\}\\)\u306f\u521d\u98051\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3042\u308b\u305f\u3081\u3001\\(a_n=r^{n-1}\\)\u3067\u3059\u3002\u307e\u305f\\(\\{b_n\\}\\)\u306f\u7b49\u5dee\u6570\u5217\u3067\u3042\u308b\u305f\u3081\u3001\\(b_n=a+(n-1)d\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\\(b_1\uff1da_3\\)\u3088\u308a<\/strong><\/p>\n<p>\\(a=r^2\\) &#8211; \u2460<\/p>\n<p><strong>\u30fb\\(b_2\uff1da_4\\)\u3088\u308a<\/strong><\/p>\n<p>\\(a+d=r^3\\) &#8211; \u2461<\/p>\n<p><strong>\u30fb\\(b_3\uff1da_2\\)\u3088\u308a<\/strong><\/p>\n<p>\\(a+2d=r\\) &#8211; \u2462<\/p>\n<p>\\(\u2461\u00d72-\u2462\\)\u3088\u308a\u3001\\(a=2r^3-r\\)\u3067\u3059\u3002\u307e\u305f\u2460\u3088\u308a\u3001\\(a=r^2\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(r^2=2r^3-r\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(r^2=2r^3-r\\)<\/p>\n<p>\\(2r^3-r^2-r=0\\)<\/p>\n<p>\\(r(2r^2-r-1)=0\\)<\/p>\n<p>\\(r(2r+1)(r-1)=0\\)<\/p>\n<p>\\(r&lt;0\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(r=-\\displaystyle\\frac{1}{2}\\)\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\\(a_n=\\left(-\\displaystyle\\frac{1}{2}\\right)^{n-1}\\)\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\\(a=r^2\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(a=\\displaystyle\\frac{1}{4}\\)\u3067\u3059\u3002\u307e\u305f\\(a+2d=r\\)\u3067\u3042\u308b\u305f\u3081\u3001\u6570\u5b57\u3092\u4ee3\u5165\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a+2d=r\\)<\/p>\n<p>\\(\\displaystyle\\frac{1}{4}+2d=-\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\\(2d=-\\displaystyle\\frac{3}{4}\\)<\/p>\n<p>\\(d=-\\displaystyle\\frac{3}{8}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(b_n=\\displaystyle\\frac{1}{4}-\\displaystyle\\frac{3}{8}(n-1)\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h3>\u7b49\u6bd4\u6570\u5217\u3068\u5bfe\u6570\u306e\u8a08\u7b97<\/h3>\n<p>\u6b21\u306e\u5fdc\u7528\u554f\u984c\u3068\u3057\u3066\u3001\u7b49\u6bd4\u6570\u5217\u3068\u5bfe\u6570\u306e\u8a08\u7b97\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002\u7b49\u6bd4\u6570\u5217\u306f\u6307\u6570\u8a08\u7b97\u306b\u306a\u308b\u305f\u3081\u3001\u9805\u6570\\(n\\)\u306e\u5024\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u3001\u7b54\u3048\u3082\u5927\u304d\u304f\u306a\u308a\u307e\u3059\uff08\u307e\u305f\u306f\u5c0f\u3055\u304f\u306a\u308a\u307e\u3059\uff09\u3002\u305d\u306e\u305f\u3081\u3001\u5bfe\u6570\u3092\u5229\u7528\u3059\u308b\u30b1\u30fc\u30b9\u304c\u3072\u3093\u3071\u3093\u306b\u3042\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u521d\u98053\u3001\u516c\u6bd42\u306e\u7b49\u6bd4\u6570\u5217\\(\\{a_n\\}\\)\u306b\u3064\u3044\u3066\u3001\\(10^4&lt;a_n&lt;10^6\\)\u3092\u6e80\u305f\u3059\\(n\\)\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\u306a\u304a\\(log_{10}2=0.3010\\)\u3067\u3042\u308a\u3001\\(log_{10}3=0.4771\\)\u3067\u3059\u3002<\/li>\n<\/ul>\n<p>\\(\\{a_n\\}\\)\u306f\u521d\u98053\u3001\u516c\u6bd42\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3042\u308b\u305f\u3081\u3001\\(a_n=3\u00b72^{n-1}\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(10^4&lt;3\u00b72^{n-1}&lt;10^6\\)\u306b\u3064\u3044\u3066\u5bfe\u6570\u3092\u52a0\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(log_{10}10^4&lt;log_{10}3\u00b72^{n-1}&lt;log_{10}10^6\\)<\/p>\n<p>\\(4log_{10}10&lt;log_{10}3+log_{10}2^{n-1}&lt;6log_{10}10\\)<\/p>\n<p>\\(4&lt;log_{10}3+(n-1)log_{10}2&lt;6\\)<\/p>\n<p>\\(4&lt;0.4771+0.3010(n-1)&lt;6\\)<\/p>\n<p>\\(4&lt;0.3010n+0.1761&lt;6\\)<\/p>\n<p>\\(3.8239&lt;0.3010n&lt;5.8239\\)<\/p>\n<p>\\(\\displaystyle\\frac{3.8239}{0.3010}&lt;n&lt;\\displaystyle\\frac{5.8239}{0.3010}\\)<\/p>\n<p>\\(12.7\u2026&lt;n&lt;19.3\u2026\\)<\/p>\n<p>\\(n\\)\u306f\u6574\u6570\u3067\u3042\u308b\u305f\u3081\u3001\\(n\\)\u306f13\u304b\u308919\u306e\u7bc4\u56f2\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u5bfe\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u7b49\u6bd4\u6570\u5217\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b<\/h2>\n<p>\u7b49\u5dee\u6570\u5217\u3068\u540c\u69d8\u306b\u6570\u5217\u3067\u57fa\u672c\u7684\u306a\u5185\u5bb9\u304c\u7b49\u6bd4\u6570\u5217\u3067\u3059\u3002\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u5f0f\u306f\u5fc5\u305a\u899a\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u899a\u3048\u306a\u3051\u308c\u3070\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u307e\u305f\u3001\u7b49\u6bd4\u4e2d\u9805\u306e\u6027\u8cea\u3082\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u3001\u7b49\u6bd4\u6570\u5217\u3067\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u308b\u516c\u5f0f\u3068\u3057\u3066\u7b49\u6bd4\u6570\u5217\u306e\u548c\u304c\u3042\u308a\u307e\u3059\u3002\u6570\u5217\u306e\u554f\u984c\u3092\u89e3\u304f\u3068\u304d\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3082\u5fc5\u305a\u899a\u3048\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u306a\u304a\u6570\u5217\u3067\u306f\u5fdc\u7528\u554f\u984c\u304c\u51fa\u3055\u308c\u307e\u3059\u3002\u7b49\u5dee\u6570\u5217\u3068\u7b49\u6bd4\u6570\u5217\u3092\u5229\u7528\u3059\u308b\u554f\u984c\u304c\u51fa\u3055\u308c\u305f\u308a\u3001\u7b49\u6bd4\u6570\u5217\u3068\u5bfe\u6570\u3092\u5229\u7528\u3059\u308b\u554f\u984c\u304c\u51fa\u984c\u3055\u308c\u305f\u308a\u3057\u307e\u3059\u3002\u305f\u3060\u3001\u6570\u5217\u304c\u4f55\u3092\u610f\u5473\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