{"id":3800,"date":"2025-12-24T17:21:35","date_gmt":"2025-12-24T08:21:35","guid":{"rendered":"https:\/\/math-travel.com\/?p=3800"},"modified":"2026-02-11T17:32:28","modified_gmt":"2026-02-11T08:32:28","slug":"touhisuuretu","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-b\/touhisuuretu\/","title":{"rendered":"\u7b49\u6bd4\u6570\u5217\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u4e00\u822c\u9805\u30fb\u548c\u306e\u6c42\u3081\u65b9\u3068\u300c\u516c\u6bd4r\u300d\u306e\u6ce8\u610f\u70b9\u3092\u89e3\u8aac"},"content":{"rendered":"\n
\u6570\u5b66B\u6570\u5217\u306e\u4e2d\u3067\u300c\u7b49\u6bd4\u6570\u5217<\/span>\u300d\u306f\u5fc5\u305a\u62bc\u3055\u3048\u3066\u304a\u304d\u305f\u3044\u6570\u5217\u3067\u3059\u3002<\/span><\/p>\n\n\n\n \u300c\u7b49\u6bd4\u6570\u5217\u306e\u57fa\u790e\u304b\u3089\u77e5\u308a\u305f\u3044\u300d <\/p>\n\n\n\n \u300c\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u3063\u3066\uff1f\u300d <\/p>\n\n\n\n \u300c\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u6c42\u3081\u65b9\u306f\uff1f\u300d<\/p>\n<\/div><\/div>\n\n\n\n \u4eca\u56de\u306f\u7b49\u6bd4\u6570\u5217\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n \u7b49\u6bd4\u6570\u5217\u306f\u5206\u304b\u308b\u3051\u3069\u3001\u548c\u306e\u516c\u5f0f\u304c\u3088\u304f\u5206\u304b\u3089\u306a\u304f\u3066\u30fb\u30fb\u30fb<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u7b49\u6bd4\u6570\u5217\u3068\u306f\u300c\u4e00\u5b9a\u306e\u6bd4\u3067\u5909\u5316\u3059\u308b\u6570\u5217<\/span>\u300d<\/span>\u3092\u6307\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n \u7b49\u6bd4\u6570\u5217\u306f\u6570\u5217\u306e\u306a\u304b\u3067\u3082\u57fa\u672c\u3068\u306a\u308b\u6570\u5217\u3067\u3059\u3002<\/span><\/p>\n\n\n\n \u4e00\u822c\u9805\u3084\u548c\u3092\u6c42\u3081\u308b\u554f\u984c\u304c\u591a\u304f\u51fa\u984c\u3055\u308c\u308b\u306e\u3067\u3001\u3057\u3063\u304b\u308a\u7406\u89e3\u3057\u3066\u3044\u306a\u3044\u3068\u6570\u5217\u306e\u5358\u5143\u306f\u82e6\u6226\u3059\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u672c\u8a18\u4e8b\u3067\u306f\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u3068\u548c\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u89e3\u8aac<\/span>\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u6570\u5217\u304c\u82e6\u624b\u306a\u65b9\u3084\u3001\u3053\u308c\u304b\u3089\u6570\u5217\u3092\u5b66\u7fd2\u3059\u308b\u65b9\u306e\u53c2\u8003\u306b\u306a\u308b\u306e\u3067\u3001\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n \u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001 \u7b49\u6bd4\u6570\u5217\u3068\u306f\u300c\u4e00\u5b9a\u306e\u6bd4\u3067\u5909\u5316\u3059\u308b\u6570\u5217\u300d<\/span>\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n \u6570\u5217\u306e\u521d\u3081\u306e\u9805\u3092\u521d\u9805<\/span>\u3001\u6700\u5f8c\u306e\u9805\u3092\u672b\u9805<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305f\u3001\u7b49\u6bd4\u6570\u5217\u306b\u304a\u3044\u3066\u96a3\u308a\u5408\u3046\uff12\u3064\u306e\u9805\u306e\u6bd4\u3092\u516c\u6bd4<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n \u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6570\u5217\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n \u4e0a\u8a18\u306e\u6570\u5217\u306f\u300e\u521d\u98052\u3001\u672b\u9805486\u3001\u516c\u6bd43\u3001\u9805\u65706\u306e\u7b49\u6bd4\u6570\u5217\u300f<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n \u7b49\u6bd4\u6570\u5217\u3000\u21d2\u4e00\u5b9a\u306e\u6bd4\u3067\u5909\u5316\u3059\u308b\u6570\u5217<\/p>\n\n\n\n \u516c\u6bd4\uff1a\u96a3\u308a\u5408\u3046\u9805\u306e\u6bd4<\/p>\n\n\n\n \u521d\u9805\uff1a\u6700\u521d\u306e\u9805<\/p>\n\n\n\n \u672b\u9805\uff1a\u6700\u5f8c\u306e\u9805<\/p>\n<\/div><\/div>\n\n\n\n \u4e00\u822c\u9805\u3068\u306f\u3001\u6570\u5217\u306e\u7b2c\\(n\\)\u9805\\(a_{n}\\)\u3092\\(n\\)\u3092\u7528\u3044\u3066\u8868\u3057\u305f\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n \u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \u521d\u9805\\(a_{1}\\)\u3001\u516c\u6bd4\\(r\\)\u306e\u7b49\u6bd4\u6570\u5217\\(\\{a_{n}\\}\\)\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n \\[a_{n}=a_{1} \\cdot r^{n-1}\\]<\/p>\n<\/div><\/div>\n\n\n \u521d\u9805\u306b\u516c\u6bd4\u3092\u639b\u3051\u3066\u308b\u5f0f\u3060\u3088\u306d\uff1f<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n \u305d\u3046\u305d\u3046\uff01\u9805\u304c\u9032\u3080\u306b\u3064\u308c\u3066(r)\u306e\u6570\u304c\u5897\u3048\u3066\u3044\u304f\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u7b49\u6bd4\u6570\u5217\u306f\u521d\u9805\u306b\u5bfe\u3057\u3066\u516c\u6bd4\u3092\u639b\u3051\u3066\u3044\u304f\u6570\u5217\u3067\u3059\u3002<\/p>\n\n\n\n \u6570\u5217\\(a_{1}\u3000a_{2}\u3000a_{3}\u3000a_{4} …\u3000a_{n}\\)\u304c\u7b49\u6bd4\u6570\u5217\u3060\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u7b49\u6bd4\u6570\u5217\u306e\u516c\u6bd4\u3092\\(r\\)\u3060\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n \\(a_{1}=a_{1}\\)\u2190\u521d\u9805<\/p>\n\n\n\n \\(a_{2}=a_{1} \\times r\\)<\/p>\n\n\n\n \\(a_{3}=a_{1} \\times r^{2}\\)<\/p>\n\n\n\n \\(a_{4}=a_{1} \\times r^{3}\\)<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u306e\u3088\u3046\u306b\u521d\u9805\u306b\u516c\u5dee\u3092\u52a0\u3048\u3066\u3044\u304f\u306e\u3067\u3001<\/p>\n\n\n\n \\(a_{1}=a_{1}\\)<\/p>\n\n\n\n \\(a_{2}=a_{1} \\times r\\)<\/p>\n\n\n\n \\(a_{3}=a_{1} \\times r^{2}\\)<\/p>\n\n\n\n \uff1a<\/p>\n\n\n\n \\(a_{n}=a_{1} \\times r^{n-1}\\)<\/p>\n<\/div><\/div>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u306f\\(a_{n}=a_{1} \\cdot r^{n-1}\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n \u5177\u4f53\u7684\u306a\u6570\u5b57\u3092\u4f7f\u3063\u3066\u4e00\u822c\u9805\u3092\u8003\u3048\u3066\u307f\u3088\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u308b\u4f8b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u3053\u3053\u306b\u7b49\u6bd4\u6570\u5217\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n 2 , 6 , 18 , 54 , 162 \u2026<\/p>\n\n\n\n \u3053\u306e\u6570\u5217\u306f\u300c\u521d\u98052\u3001\u516c\u6bd43\u306e\u7b49\u6bd4\u6570\u5217\u300d\u3067\u3059\u3002<\/p>\n\n\n\n \u3053\u3053\u3067\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u306e\u516c\u5f0f\u3092\u601d\u3044\u51fa\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u521d\u9805\\(a_{1}\\)\u3001\u516c\u6bd4\\(d\\)\u306e\u7b49\u6bd4\u6570\u5217\u3092\\(\\{a_{n}\\}\\)\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n \\(a_{n}=a_{1} \\cdot r^{n-1}\\)<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u306e\u6570\u5217\u306f\u521d\u98052\u3001\u516c\u6bd43\u306e\u6570\u5217\u306a\u306e\u3067\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001\u7b49\u6bd4\u6570\u5217\uff5b2 , 6 , 18 , 54 , 162 \u2026\uff5d\u306e\u4e00\u822c\u9805\u306f\\(a_{n}=2 \\cdot 3^{n-1}\\)<\/p>\n\n\n \u6c42\u3081\u305f\u4e00\u822c\u9805\u304c\u5408\u3063\u3066\u3044\u308b\u304b\u5fc3\u914d\u306a\u3068\u304d\u306f\u3001\u5b9f\u969b\u306b\u4ee3\u5165\u3057\u3066\u78ba\u304b\u3081\u3066\u307f\u3088\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u6c42\u3081\u305f\u4e00\u822c\u9805\u304c\u4e0d\u5b89\u306a\u3068\u304d\u306f\u5177\u4f53\u7684\u306a\u6570\u5b57\u3092\u4ee3\u5165\u3057\u3066\u78ba\u304b\u3081\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \u521d\u9805\u304c2\u306a\u306e\u3067\u3001\u4e00\u822c\u9805\u306b\\(n=1\\)\u3092\u4ee3\u5165\u3057\u30662\u306b\u306a\u308c\u3070\u5927\u4e08\u592b\u3067\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \\(n=1\\)\u306e\u3068\u304d\u521d\u9805\u3068\u540c\u3058\u5024\u306b\u306a\u3063\u305f\u306e\u3067\u9593\u9055\u3044\u306a\u3055\u305d\u3046\u3067\u3059\u3002<\/p>\n\n\n\n \u6570\u5217\u306e\u9805\u3092\u8db3\u3059\u3053\u3068\u3092\u6570\u5217\u306e\u548c\u3068\u3044\u3044\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \u7b49\u6bd4\u6570\u5217{3 , 6 , 12 , 24}\u306e\u521d\u9805\u304b\u3089\u7b2c4\u9805\u307e\u3067\u306e\u548c\u306f26\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n 3+6+12+24=45<\/p>\n\n\n\n \u3053\u306e\u3088\u3046\u306b\u7b49\u6bd4\u6570\u5217\u306e\u548c\u3092\u6c42\u3081\u308b\u554f\u984c\u306f\u3088\u304f\u51fa\u984c\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n \u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u306f\u516c\u6bd4\u306e\u5024\u306b\u3088\u3063\u3066\u5909\u308f\u308a\u307e\u3059\u3002\u8907\u96d1\u3067\u3059\u304c\u78ba\u5b9f\u306b\u899a\u3048\u3066\u304a\u304d\u305f\u3044\u516c\u5f0f<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n \u521d\u9805\\(a\\)\u3001\u516c\u5dee\\(d\\)\u3001\u9805\u6570\\(n\\)\u306e\u7b49\u6bd4\u6570\u5217\u306e\u548c\u3092\\(S_{n}\\)\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n [1]\\(r <1\\)\u306e\u3068\u304d<\/p>\n\n\n\n \\[\\displaystyle S_{n}=\\frac{a(1-r^{n})}{1-r}\\]<\/p>\n\n\n\n [2]\\(r \uff1e 1\\)\u306e\u3068\u304d<\/p>\n\n\n\n \\[\\displaystyle S_{n}=\\frac{a(r^{n}-1)}{r-1}\\]<\/p>\n\n\n\n [3]\\(r=1\\)\u306e\u3068\u304d<\/p>\n\n\n\n \\[S_{n}=na\\]<\/p>\n<\/div><\/div>\n\n\n\n \u5b9f\u969b\u306b\u7b49\u6bd4\u6570\u5217\u306e\u548c\u30922\u3064\u306e\u3084\u308a\u65b9\u3067\u6c42\u3081\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u3088\u3046\u306a\u7b49\u6bd4\u6570\u5217\u304c\u3042\u3063\u305f\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n \u3053\u306e\u6570\u5217\u306f\u300c\u521d\u98055\u3001\u516c\u6bd43\u3001\u9805\u65706\u306e\u7b49\u6bd4\u6570\u5217\u300d\u3067\u3059\u3002<\/p>\n\n\n\n \u516c\u6bd4\u304c3\u30671\u3088\u308a\u5927\u304d\u3044\u306e\u3067\u3053\u306e\u516c\u5f0f\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\displaystyle S_{n}=\\frac{a(r^{n}-1)}{r-1}\\]<\/p>\n\n\n\n \u521d\u98055\u3001\u516c\u6bd43\u3001\u9805\u65706\u306e\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306f<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \u516c\u6bd4\\(r\\)\u304c1\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u306f\u3053\u306e\u516c\u5f0f\u3067\u6c42\u3081\u308b\u3002<\/p>\n\n\n\n \\[\\displaystyle S_{n}=\\frac{a(r^{n}-1)}{r-1}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u516c\u6bd4\u304c1\u306e\u5834\u5408\u306e\u7b49\u6bd4\u6570\u5217\u306e\u548c\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n \\(r = 1\\)\u306e\u5834\u5408\u306f\u540c\u3058\u6570\u5b57\u304c\u4e26\u3073\u7d9a\u3051\u308b\u6570\u5217\u3067\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u6570\u5217\u306e\u548c\u306f\uff08\u521d\u9805\uff09\u00d7\uff08\u9805\u6570\uff09\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001\\(r=1\\)\u306e\u3068\u304d\u306f\u3053\u306e\u516c\u5f0f\u3092\u4f7f\u3044\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\[\\displaystyle S_{n}=na\\]<\/p>\n\n\n\n \u4eca\u56de\u306f\u521d\u98055\u3001\u9805\u65706\u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u516c\u6bd4\\(r\\)\u304c1\u306e\u5834\u5408\u306f\u3053\u306e\u516c\u5f0f\u3067\u6c42\u3081\u308b\u3002<\/p>\n\n\n\n \\[\\displaystyle S_{n}=na\\]<\/p>\n<\/div><\/div>\n\n\n \u516c\u6bd4\u306e\u5024\u304c\u5206\u304b\u308c\u3070\u3001\u3042\u3068\u306f\u4ee3\u5165\u3059\u308b\u3060\u3051\u306a\u3093\u3060\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u03a3\uff08\u30b7\u30b0\u30de\uff09\u3068\u306f\u6570\u5b66\u306e\u8a18\u53f7\u306e1\u3064\u3067\u3059\u3002<\/p>\n\n\n\n \u6570\u5217\\(a_{n}\\)\u306e\u521d\u9805\u304b\u3089\u7b2c\\(n\\)\u9805\u307e\u3067\u8db3\u3059\u3053\u3068\u3092\u8a18\u53f7\u03a3\uff08\u30b7\u30b0\u30de\uff09\u3092\u7528\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\sum_{k=1}^{n} a_{k}=a_{1}+a_{2}+a_{3}+\\cdots+a_{n}\\]<\/p>\n\n\n\n \\(\\sum_{k=1}^{n}\\)\u306e\u898b\u305f\u76ee\u304c\u96e3\u3057\u305d\u3046\u306a\u306e\u3067\u8eab\u69cb\u3048\u3066\u3057\u307e\u3044\u307e\u3059\u304c\u3001\u30b7\u30b0\u30de\u306e\u610f\u5473\u306f\u300ck=1\u304b\u3089n\u307e\u3067\u4ee3\u5165\u3057\u305f\u3082\u306e\u3092\u8db3\u3059\u300d<\/span>\u3068\u3044\u3046\u3060\u3051\u3067\u3059\u3002<\/p>\n\n\n\n \u30b7\u30b0\u30de\u03a3\u306e\u516c\u5f0f\u3084\u8a08\u7b97\u306b\u3064\u3044\u3066\u306f\u300c\u03a3\u30b7\u30b0\u30de\u306e\u8a08\u7b97\u516c\u5f0f\u3068\u8a3c\u660e\uff01\u6570\u5217\u306e\u548c\u304c\u4e00\u77ac\u3067\u89e3\u3051\u308b\uff01\u300d\u3067\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u4ee5\u4e0b\u306e\u3088\u3046\u306a\u03a3\u306e\u8a08\u7b97\u306f\u3001\u7b49\u6bd4\u6570\u5217\u306e\u548c\u3068\u3057\u3066\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\sum_{k=1}^{n} r^{k}=\\displaystyle \\frac{r(r^{n}-1)}{r-1}= \\frac{r(1-r^{n})}{1-r}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u306a\u305c\u3053\u306e\u03a3\u306e\u8a08\u7b97\u304c\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306b\u306a\u308b\u306e\u304b\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305a\u5de6\u8fba\u306e\u03a3\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3068\u3001<\/p>\n\n\n\n \\[\\sum_{k=1}^{n} r^{k}=r+r^{2}+r^{3}+ \\cdots + r^{n}\\]<\/p>\n\n\n\n \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u308c\u306f\u300c\u521d\u9805r\u3001\u516c\u6bd4r\u3001\u9805\u6570n\u306e\u7b49\u6bd4\u6570\u5217\u306e\u548c\u300d\u3068\u540c\u3058\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u306d\u3002<\/p>\n\n\n\n \u305d\u3053\u3067\u53f3\u8fba\u306f\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u3053\u308c\u3067\u7b49\u6bd4\u6570\u5217\u306e\u03a3\u3092\u548c\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/p>\n\n\n\n \u3067\u306f\u30011\u554f\u3060\u3051\u03a3\u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u6b21\u306e\u5024\u3092\u6c42\u3081\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n \\[\\sum_{k=1}^{6} 3^{k}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u308c\u304c\u610f\u5473\u3059\u308b\u306e\u306f\u3001\\(\\{3+9+27+\\cdots+729\\}\\)\u306a\u306e\u3067\u3001\u300c\u521d\u98053\u3001\u672b\u9805729\u3001\u9805\u65706\u306e\u7b49\u6bd4\u6570\u5217\u306e\u548c\u300d\u3068\u3057\u3066\u8003\u3048\u308b\u3068\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u7b49\u6bd4\u6570\u5217\u306e\u6f38\u5316\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f62\u3067\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u6570\u5217\u306b\u304a\u3051\u308b\u7b2c\\(n\\)\u9805\u3092\\(a_{n}\\)\u3001\u516c\u6bd4\u3092\\(r\\)\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n \\[a_{n+1}=ra_{n}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u6f38\u5316\u5f0f\u3068\u306f\u3001\u6570\u5217\u306e\u7b2c\\(n\\)\u9805\\(a_{n}\\)\u3092\u7528\u3044\u3066\u6b21\u306e\u9805\u3067\u3042\u308b\\(a_{n+1}\\)\u3092\u8868\u3057\u305f\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n \u7b49\u6bd4\u6570\u5217\u306e\u6f38\u5316\u5f0f\u306f\u3001\\(a_{n}\\)\u306b\u516c\u6bd4\\(r\\)\u3092\u639b\u3051\u308b\u3053\u3068\u3067\\(a_{n+1}\\)\u306b\u306a\u308b\u3053\u3068\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u5b9f\u969b\u306b\u6570\u5b57\u3092\u5165\u308c\u3066\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n <\/span><\/p>\n\n\n\n \u3053\u3053\u306b\u521d\u98052\u3001\u516c\u6bd43\u306e\u7b49\u6bd4\u6570\u5217\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u6570\u5217\u306f\u521d\u9805\u306b\u5bfe\u3057\u3066\u30013\u500d\u305a\u3064\u5909\u5316\u3057\u3066\u3044\u304f\u306e\u3067<\/p>\n\n\n\n \\(a_{1}=2\\)<\/p>\n\n\n\n \\(a_{2}=3 \\cdot a_{1}\\)<\/p>\n\n\n\n \\(a_{3}=3 \\cdot a_{2}\\)<\/p>\n\n\n\n \\(a_{4}=3 \\dot a_{3}\\)<\/p>\n\n\n\n \u3068\u3044\u3046\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u306e\u3088\u3046\u306b\\(a_{n+1}\\)\u306e\u9805\u3092\u8868\u3059\u3068\u304d\u306f\u3001\\(a_{n}\\)\u30923\u500d\u3059\u308c\u3070\u826f\u3044\u306e\u3067\u3001<\/p>\n\n\n\n \\[a_{n+1}=3a_{n}\\]<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001\u7b49\u6bd4\u6570\u5217\u306e\u6f38\u5316\u5f0f\u306f\u4ee5\u4e0b\u306e\u5f62\u3067\u8868\u3055\u308c\u308b\u3002<\/p>\n\n\n\n \u6570\u5217\u306b\u304a\u3051\u308b\u7b2c\\(n\\)\u9805\u3092\\(a_{n}\\)\u3001\u516c\u6bd4\u3092\\(r\\)\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n \\[a_{n+1}=ra_{n}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u7b49\u6bd4\u6570\u5217\u306e\u6027\u8cea\u306e1\u3064\u306b\u201d\u7b49\u6bd4\u4e2d\u9805\u201d\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u6570\u5217\\(a,b,c\\)\u304c\u7b49\u6bd4\u6570\u5217\u306e\u3068\u304d\u3001<\/p>\n\n\n\n \\[b^{2}=ac\\]<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u308c\u306f\u7b49\u6bd4\u6570\u5217\u306e\u98053\u3064\u7528\u610f\u3057\u305f\u3068\u304d\u306b\u3001\u4e21\u7aef\u306e\u9805\u306e\u7a4d\u304c\u4e2d\u592e\u306e\u9805\u306e2\u4e57\u306b\u306a\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u8a3c\u660e\u306f\u975e\u5e38\u306b\u7c21\u5358\u3067\u3059\u3002\\(a,b,c\\)\u306f\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067<\/p>\n\n\n\n \\[\\displaystyle \\frac{b}{a}=\\frac{c}{b}\\]<\/p>\n\n\n\n \u4e21\u8fba\u306bab\u3092\u639b\u3051\u3066\u3001<\/p>\n\n\n\n \\[b^{2}=ac\\]<\/p>\n\n\n\n \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u4eca\u56de\u306f\u7b49\u6bd4\u6570\u5217\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u6570\u5217\u306b\u306f\u7b49\u6bd4\u6570\u5217\u4ee5\u5916\u306b\u3082\u4ee5\u4e0b\u306e\u6570\u5217\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u30fb\u7b49\u5dee\u6570\u5217<\/span><\/p>\n\n\n\n \u7b49\u5dee\u6570\u5217\u3068\u306f\u3001\u300c\u4e00\u5b9a\u306e\u5dee\u3067\u5909\u5316\u3059\u308b\u6570\u5217\u300d<\/span>\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n \u7b49\u5dee\u6570\u5217\u306b\u3064\u3044\u3066\u306f\u3001\u300c\u7b49\u5dee\u6570\u5217\u306e\u516c\u5f0f\u307e\u3068\u3081\uff01\u4e00\u822c\u9805\u3068\u548c\u306e\u516c\u5f0f\u3092\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\uff01\u300d\u3067\u8a73\u3057\u304f\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u30fb\u968e\u5dee\u6570\u5217<\/span><\/p>\n\n\n\n \u968e\u5dee\u6570\u5217\u306f\u8907\u96d1\u3067\u3001\u5404\u9805\u306e\u5dee\u3092\u66f8\u304d\u51fa\u3057\u3066\u307f\u308b\u3068\u3042\u308b\u6570\u5217\u304c\u898b\u3048\u3066\u304d\u307e\u3059\u3002<\/p>\n\n\n \u4e0a\u306e\u6570\u5217\u306e\u5834\u5408\u3001\u5404\u9805\u306e\u5dee\u304c\u7b49\u5dee\u6570\u5217\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \u3053\u306e\u5dee\u304c\u7b49\u6bd4\u6570\u5217\u306b\u306a\u308b\u5834\u5408\u3082\u3042\u308a\u307e\u3059\u3057\u3001\u3082\u3063\u3068\u8907\u96d1\u306a\u6570\u5217\u306b\u306a\u308b\u3068\u304d\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u968e\u5dee\u6570\u5217\u306b\u3064\u3044\u3066\u306f\u3001\u300c\u968e\u5dee\u6570\u5217\u3092\u7528\u3044\u305f\u4e00\u822c\u9805\u3068\u548c\u3092\u6c42\u3081\u308b\u516c\u5f0f\uff01\u521d\u9805\u306b\u968e\u5dee\u3092\u8db3\u3057\u3066\u3044\u304f\u3060\u3051\u300d\u3067\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u3084\u548c\u306e\u6c42\u3081\u65b9\u3092\u78ba\u8a8d\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \u5b9f\u969b\u306b\u6570\u5b57\u3092\u4f7f\u3063\u3066\u3001\u4e00\u822c\u9805\u3084\u548c\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u6b21\u306e\u6570\u5217\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n\n\n\n 2, 10 , 50 , 250 , 1250 \u2026<\/p>\n<\/div><\/div>\n\n\n\n \u4e0e\u3048\u3089\u308c\u305f\u6570\u5217\u306f\u300c\u521d\u98052\u3001\u516c\u6bd45\u306e\u7b49\u6bd4\u6570\u5217\u300d\u3067\u3059\u3002<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001\u6c42\u3081\u308b\u4e00\u822c\u9805\u306f<\/p>\n\n\n\n \\[a_{n}=2 \\cdot 5^{n-1}\\]<\/p>\n\n\n\n \u21d2<a href=”#an”>\u4e00\u822c\u9805\u306e\u6c42\u3081\u65b9\u3092\u5fd8\u308c\u305f\u65b9<\/a><\/p>\n<\/div><\/details>\n<\/div>\n\n\n\n \u6b21\u306e\u6570\u5217\u306e\u521d\u9805\u304b\u3089\u7b2c(n)\u9805\u307e\u3067\u306e\u548c\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n\n\n\n 3 , 6 , 12 , 24 , 48 \u2026<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u308c\u306f\u300c\u521d\u98053\u3001\u516c\u6bd42\u3001\u9805\u6570n\u306e\u7b49\u6bd4\u6570\u5217\u306e\u548c\u300d\u3067\u3059\u3002<\/p>\n\n\n\n \u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001\u4eca\u56de\u6c42\u3081\u308b\u548c\u306f<\/p>\n\n\n\n \\[S_{n}=3 \\cdot 2^{n} -3\\]<\/p>\n\n\n\n \u21d2<a href=”#wa”>\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u5fd8\u308c\u305f\u65b9<\/a><\/p>\n<\/div><\/details>\n<\/div>\n\n\n\n \u4eca\u56de\u306f\u7b49\u6bd4\u6570\u5217\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n \u7b49\u6bd4\u6570\u5217\u3068\u306f<\/span> \u521d\u9805\\(a_{1}\\)\u3001\u516c\u6bd4\\(r\\)\u306e\u7b49\u6bd4\u6570\u5217\\(\\{a_{n}\\}\\)\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n \\[a_{n}=a_{1} \\cdot r^{n-1}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u521d\u9805\\(a\\)\u3001\u516c\u5dee\\(d\\)\u3001\u9805\u6570\\(n\\)\u306e\u7b49\u6bd4\u6570\u5217\u306e\u548c\u3092\\(S_{n}\\)\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n [1]\\(r < 1\\)\u306e\u3068\u304d<\/p>\n\n\n\n \\[\\displaystyle S_{n}=\\frac{a(1-r^{n})}{1-r}\\]<\/p>\n\n\n\n [2]\\(r > 1\\)\u306e\u3068\u304d<\/p>\n\n\n\n \\[\\displaystyle S_{n}=\\frac{a(r^{n}-1)}{r-1}\\]<\/p>\n\n\n\n [3]\\(r=1\\)\u306e\u3068\u304d<\/p>\n\n\n\n \\[S_{n}=na\\]<\/p>\n<\/div><\/div>\n\n\n\n \u672c\u8a18\u4e8b\u3067\u306f\u7b49\u6bd4\u6570\u5217\u3092\u30e1\u30a4\u30f3\u306b\u89e3\u8aac\u3057\u307e\u3057\u305f\u304c\u3001\u7b49\u5dee\u6570\u5217\u3084\u968e\u5dee\u6570\u5217\u3082\u91cd\u8981\u306a\u6570\u5217<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n \u3053\u306e3\u3064\u306e\u6570\u5217\u306f\u78ba\u5b9f\u306b\u62bc\u3055\u3048\u3066\u304a\u304b\u306a\u3044\u3068\u3001\u6f38\u5316\u5f0f\u3084\u7fa4\u6570\u5217\u3092\u5b66\u7fd2\u3059\u308b\u3068\u304d\u306b\u82e6\u6226\u3059\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u6570\u5b66B\u6570\u5217\u306e\u4e2d\u3067\u300c\u7b49\u6bd4\u6570\u5217\u300d\u306f\u5fc5\u305a\u62bc\u3055\u3048\u3066\u304a\u304d\u305f\u3044\u6570\u5217\u3067\u3059\u3002 \u4eca\u56de\u306f\u7b49\u6bd4\u6570\u5217\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u3066\u3044\u304d\u307e\u3059\u3002 \u7b49\u6bd4\u6570\u5217\u3068\u306f\u300c\u4e00\u5b9a\u306e\u6bd4\u3067\u5909\u5316\u3059\u308b\u6570\u5217\u300d\u3092\u6307\u3057\u307e\u3059\u3002 \u7b49\u6bd4\u6570\u5217\u306f\u6570\u5217\u306e\u306a\u304b\u3067\u3082\u57fa\u672c\u3068\u306a\u308b\u6570\u5217\u3067\u3059\u3002 \u4e00\u822c\u9805\u3084\u548c\u3092 […]<\/p>\n","protected":false},"author":1,"featured_media":6213,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[47,225],"tags":[48,14,11],"class_list":["post-3800","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-suuretu","category-math-b","tag-48","tag-b","tag-11"],"yoast_head":"\n
\u9ad8\u6821\u751f<\/span><\/div>
<\/figure>\n<\/div>\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>
\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n\u7b49\u6bd4\u6570\u5217\u3068\u306f\uff1f<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n\u7b49\u6bd4\u6570\u5217\u3092\u4e00\u822c\u9805\u3067\u8868\u3059<\/h2>\n\n\n\n
\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u306e\u516c\u5f0f<\/h3>\n\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u306e\u8a3c\u660e<\/h3>\n\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u308b<\/h3>\n\n\n\n
a_{n}&=&a_{1} \\times r^{n-1}\\\\
&=&2 \\times 3^{n-1}\\\\
&=&2 \\cdot 3^{n-1}
\\end{eqnarray}<\/p>\n\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>
a_{1}&=&2 \\times 3^{1-1}\\\\
&=&2 \\times 1\\\\
&=&2
\\end{eqnarray}<\/p>\n\n\n\n\u7b49\u6bd4\u6570\u5217\u306e\u548c<\/h2>\n\n\n\n
\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f<\/h3>\n\n\n\n
\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u2460<\/h3>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
\\displaystyle S_{6}&=&\\frac{a(r^{n}-1)}{r-1}\\\\
&=&\\frac{5(3^{6}-1)}{3-1}\\\\
&=&\\frac{5(729-1)}{2}
&=&1820
\\end{eqnarray}<\/p>\n\n\n\n\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u2461<\/h3>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
\\displaystyle S_{6}&=&5 \\times 6\\\\
&=&30
\\end{eqnarray}<\/p>\n\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\u7b49\u6bd4\u6570\u5217\u306e\u03a3<\/h2>\n\n\n\n
\u305d\u3082\u305d\u3082\u03a3\uff08\u30b7\u30b0\u30de\uff09\u3068\u306f<\/h3>\n\n\n\n
\u7b49\u6bd4\u6570\u5217\u306e\u03a3<\/h3>\n\n\n\n
\\sum_{k=1}^{n} r^{k}&=&r+r^{2}+r^{3}+ \\cdots + r^{n}\\\\
\\displaystyle &=&\\frac{r(r^{n}-1)}{r-1}
\\end{eqnarray}<\/p>\n\n\n\n\u7b49\u6bd4\u6570\u5217\u306e\u03a3\u306e\u8a08\u7b97<\/h3>\n\n\n\n
\\sum_{k=1}^{6} 3^{k}&=&3+9+27+ \\cdots + 729\\\\
\\displaystyle &=&\\frac{3(3^{6}-1)}{3-1}\\\\
\\displaystyle &=&\\frac{3(729-1)}{2}\\\\
&=&1092
\\end{eqnarray}<\/p>\n\n\n\n\u7b49\u6bd4\u6570\u5217\u306e\u6f38\u5316\u5f0f<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\u7b49\u6bd4\u6570\u5217\u306e\u6027\u8cea<\/h2>\n\n\n\n
\u305d\u306e\u4ed6\u306e\u6570\u5217<\/h2>\n\n\n\n
\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n\u7b49\u6bd4\u6570\u5217\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n
\u89e3\u7b54<\/span><\/i><\/i><\/span><\/summary>
<\/span><\/i><\/i><\/span><\/summary>
\u89e3\u7b54<\/span><\/i><\/i><\/span><\/summary>
\\displaystyle S_{n}&=&\\frac{a_{1}(r^{n}-1)}{r-1}\\\\
&=&\\frac{3(2^{n}-1)}{2-1}\\\\
&=&3 \\cdot 2^{n} -3
\\end{eqnarray}<\/p>\n\n\n\n\u7b49\u6bd4\u6570\u5217\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n
\u21d2\u4e00\u5b9a\u306e\u6bd4\u3067\u5909\u5316\u3059\u308b\u6570\u5217<\/p>\n\n\n\n