{"id":12099,"date":"2023-01-06T14:15:32","date_gmt":"2023-01-06T05:15:32","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=12099"},"modified":"2023-01-12T09:37:02","modified_gmt":"2023-01-12T00:37:02","slug":"recurrence-relation-3","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/recurrence-relation-3.html","title":{"rendered":"\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\uff1a\u7279\u6027\u65b9\u7a0b\u5f0f\u3067\u306e\u516c\u5f0f\u3068\u968e\u5dee\u6570\u5217\u30fb\u91cd\u89e3"},"content":{"rendered":"\n<p>\u6f38\u5316\u5f0f\u3067\u306f\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u79c1\u305f\u3061\u304c\u5b66\u3076\u7279\u6b8a\u306a\u6f38\u5316\u5f0f\u3068\u3057\u3066\u3001\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306b\u95a2\u3059\u308b\u554f\u984c\u3082\u5b58\u5728\u3057\u307e\u3059\u3002\u9023\u7d9a\u3059\u308b3\u3064\u306e\u9805\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6f38\u5316\u5f0f\u304c\u5f62\u6210\u3055\u308c\u308b\u306e\u3067\u3059\u3002\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306e\u554f\u984c\u3092\u89e3\u304f\u3068\u304d\u3001\u65b9\u6cd5\u304c\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u554f\u984c\u3092\u89e3\u3051\u308b\u304b\u3069\u3046\u304b\u3068\u3044\u3046\u306e\u306f\u3001\u89e3\u304d\u65b9\u3092\u77e5\u3063\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306f3\u30d1\u30bf\u30fc\u30f3\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u305d\u308c\u305e\u308c\u306e\u30d1\u30bf\u30fc\u30f3\u3092\u899a\u3048\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306b\u3064\u3044\u3066\u306f\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u3066\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306b\u95a2\u3059\u308b\u77e5\u8b58\u3082\u5fc5\u8981\u306b\u306a\u308b\u305f\u3081\u3001\u6f38\u5316\u5f0f\u3067\u5fc5\u8981\u306a\u77e5\u8b58\u3092\u3059\u3079\u3066\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3068\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f<\/h2>\n<p>\u4e21\u96a3\u306b\u5b58\u5728\u3059\u308b\u9805\u3092\u5229\u7528\u3057\u3066\u8868\u3059\u306e\u304c\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306f\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+1}=3a_n+4\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\\(a_n\\)\u3068\\(a_{n+1}\\)\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u6f38\u5316\u5f0f\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e00\u65b9\u3067\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f0f\u304c\u8a72\u5f53\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+2}-3a_{n+1}+2a_n=0\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\\(a_n\\)\u3001\\(a_{n+1}\\)\u3001\\(a_{n+2}\\)\u30683\u3064\u306e\u9023\u7d9a\u3059\u308b\u9805\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5f0f\u304c\u8868\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h3>\u96a3\u63a53\u9805\u9593\u3067\u5229\u7528\u3055\u308c\u308b\u7279\u6027\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u6f38\u5316\u5f0f\u3092\u5909\u5f62\u3057\u3001\u4e00\u822c\u9805\u3092\u5f97\u3089\u308c\u308b\u5f62\u306b\u3059\u308b\u305f\u3081\u306b\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306b\u3064\u3044\u3066\u3082\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d<span style=\"color: #0000ff;\">\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3067\u306f\u3001\\(a_n=1\\)\u3001\\(a_{n+1}=x\\)\u3001\\(a_{n+2}=x^2\\)\u3068\u307f\u306a\u3057\u307e\u3059\u3002<\/span>\u3053\u306e\u3088\u3046\u306b\u8003\u3048\u308b\u3068\u3001\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3068\u540c\u69d8\u306b\u3001\u6f38\u5316\u5f0f\u3092\u6700\u9069\u306a\u5f62\u3078\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3089\u3067\u3059\u3002\u4f8b\u3048\u3070\\(a_{n+2}-3a_{n+1}+2a_n=0\\)\u3067\u3042\u308c\u3070\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x^2-3x+2=0\\)<\/li>\n<\/ul>\n<p>\u56e0\u6570\u5206\u89e3\u3059\u308b\u3068\\((x-1)(x-2)=0\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(x=1,2\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3067\u306f\\(x=1\\)\u306e\u3068\u304d\u3001\\(x=2\\)\u306e\u3068\u304d\u306e2\u30d1\u30bf\u30fc\u30f3\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306b\u3064\u3044\u3066\u3001\u4e8c\u6b21\u65b9\u7a0b\u5f0f\\(px^2+qx+r=0\\)\u306e\u89e3\u3092\u03b1\u3001\u03b2\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+2}-\u03b1a_{n+1}=\u03b2(a_{n+1}-\u03b1a_n)\\)<\/li>\n<li>\\(a_{n+2}-\u03b2a_{n+1}=\u03b1(a_{n+1}-\u03b2a_n)\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u95a2\u4fc2\u306f\u899a\u3048\u3066\u3057\u307e\u3044\u307e\u3057\u3087\u3046\u3002\u53c2\u8003\u307e\u3067\u306b\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u3053\u306e\u5f0f\u3078\u5909\u5f62\u3067\u304d\u308b\u3053\u3068\u3092\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u6bce\u56de\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3057\u3066\u516c\u5f0f\u3092\u5f97\u308b\u306e\u306f\u5927\u5909\u3067\u3042\u308b\u305f\u3081\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u5f0f\u306e\u5909\u5f62\u6cd5\u3092\u899a\u3048\u308b\u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u5f0f\\(a_{n+2}-3a_{n+1}+2a_n=0\\)\u3067\u3042\u308c\u3070\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\\(x=1,2\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+2}-a_{n+1}=2(a_{n+1}-a_n)\\)<\/li>\n<li>\\(a_{n+2}-2a_{n+1}=a_{n+1}-2a_n\\)<\/li>\n<\/ul>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u5229\u7528\u6cd5\u3092\u899a\u3048\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u3001\u3053\u306e\u516c\u5f0f\u3092\u899a\u3048\u308b\u306e\u306f\u5fc5\u9808\u3067\u3059\u3002<\/p>\n<h2>\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3092\u89e3\u304f\u65b9\u91dd<\/h2>\n<p>\u6f38\u5316\u5f0f\u306f\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u304a\u308a\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3092\u89e3\u304f\u65b9\u6cd5\u3082\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u524d\u8ff0\u306e\u901a\u308a\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306b\u3064\u3044\u3066\u3082\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u3088\u3063\u3066\u554f\u984c\u306e\u89e3\u304d\u65b9\u306e\u65b9\u91dd\u304c\u7570\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u5177\u4f53\u7684\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30d1\u30bf\u30fc\u30f3\u5206\u3051\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b1\u3092\u542b\u3080\u5834\u5408<\/li>\n<li>\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b1\u3092\u542b\u307e\u306a\u3044\u5834\u5408<\/li>\n<li>\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u304c\u91cd\u89e3\u306e\u5834\u5408<\/li>\n<\/ul>\n<p>\u3059\u3079\u3066\u306e\u89e3\u304d\u65b9\u3092\u899a\u3048\u308c\u3070\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u89e3\u304d\u65b9\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b1\u3092\u542b\u3080\u5834\u5408\u3001\u968e\u5dee\u6570\u5217\u3092\u7528\u3044\u308b<\/h3>\n<p>\u307e\u305a\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b1\u3092\u542b\u3080\u30b1\u30fc\u30b9\u3092\u78ba\u8a8d\u3057\u3066\u3044\u304d\u307e\u3059\u3002<span style=\"color: #ff0000;\">\u3053\u306e\u5834\u5408\u3001\u968e\u5dee\u6570\u5217\u3092\u5229\u7528\u3067\u304d\u307e\u3059\u3002<\/span>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(a_1=2\\)\u3001\\(a_2=7\\)\u3001\\(a_{n+2}-3a_{n+1}+2a_n=0\\)\u306b\u3088\u3063\u3066\u5b9a\u3081\u3089\u308c\u308b\u6570\u5217\\(\\{a_n\\}\\)\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u901a\u308a\u3001\\(a_{n+2}-3a_{n+1}+2a_n=0\\)\u306b\u3064\u3044\u3066\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u306f\\(x^2-3x+2=0\\)\u3067\u3059\u3002\u307e\u305f\u3001\\(x^2-3x+2=0\\)\u306e\u89e3\u306f\\(x=1,2\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u65b9\u7a0b\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+2}-a_{n+1}=2(a_{n+1}-a_n)\\)<\/li>\n<li>\\(a_{n+2}-2a_{n+1}=a_{n+1}-2a_n\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3046\u3061\\(x=1\\)\u306e\u3068\u304d\u3001\u3064\u307e\u308a\u4ee5\u4e0b\u306e\u6f38\u5316\u5f0f\u306b\u7740\u76ee\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(a_{n+2}-a_{n+1}=2(a_{n+1}-a_n)\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u6f38\u5316\u5f0f\u3067\u306f\u3001\u968e\u5dee\u6570\u5217\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u968e\u5dee\u6570\u5217\\(\\{a_{n+1}-a_n\\}\\)\u306f\u521d\u9805\\(a_2-a_1=5\\)\u3001\u516c\u6bd42\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u968e\u5dee\u6570\u5217\u306e\u4e00\u822c\u9805\u306f\\(5\u00b72^{n-1}\\)\u3067\u3059\u3002\u307e\u305f\u3001\u968e\u5dee\u6570\u5217\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e00\u822c\u9805\\(a_n\\)\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(a_n=2+\\displaystyle\\sum_{k=1}^{n-1}{5\u00b72^{k-1}}\\)<\/p>\n<p>\\(a_n=2+\\displaystyle\\frac{5(2^{n-1}-1)}{2-1}\\)<\/p>\n<p>\\(a_n=5\u00b72^{n-1}-3\\)<\/p>\n<p>\u306a\u304a\\(n=1\\)\u306e\u3068\u304d\u3001\\(a_1=2\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(a_n=5\u00b72^{n-1}-3\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u968e\u5dee\u6570\u5217\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u4e00\u822c\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b1\u304c\u542b\u307e\u308c\u308b\u5834\u5408\u3001\u968e\u5dee\u6570\u5217\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u968e\u5dee\u6570\u5217\u306e\u516c\u5f0f\u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b1\u3092\u542b\u307e\u306a\u3044\u5834\u5408\u306e\u89e3\u304d\u65b9<\/h3>\n<p>\u6b21\u306b\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b1\u3092\u542b\u307e\u306a\u3044\u30b1\u30fc\u30b9\u306e\u89e3\u304d\u65b9\u3092\u78ba\u8a8d\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u5834\u5408\u306f\u968e\u5dee\u6570\u5217\u3092\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u306e\u4ee3\u308f\u308a\u30012\u3064\u306e\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b49\u6bd4\u6570\u5217\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u306e\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(a_1=0\\)\u3001\\(a_2=1\\)\u3001\\(a_{n+2}=a_{n+1}+6a_n\\)\u306b\u3088\u3063\u3066\u5b9a\u3081\u3089\u308c\u308b\u6570\u5217\\(\\{a_n\\}\\)\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\u3044\u3046\u65b9\u91dd\u306f\u540c\u3058\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x^2-x-6=0\\)<\/p>\n<p>\\((x-3)(x+2)\\)<\/p>\n<p>\\(x=-2,3\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u6f38\u5316\u5f0f\u3078\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+2}+2a_{n+1}=3(a_{n+1}+2a_n)\\)<\/li>\n<li>\\(a_{n+2}-3a_{n+1}=-2(a_{n+1}-3a_n)\\)<\/li>\n<\/ul>\n<p>\\(a_{n+2}+2a_{n+1}=3(a_{n+1}+2a_n)\\)\u3092\u78ba\u8a8d\u3059\u308b\u3068\u3001\u6570\u5217\\(\\{a_{n+1}+2a_n\\}\\)\u306f\u521d\u9805\\(a_2+2a_1=1\\)\u3001\u516c\u6bd43\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+1}+2a_n=3^{n-1}\\) &#8211; \u2460<\/li>\n<\/ul>\n<p>\u307e\u305f\\(a_{n+2}-3a_{n+1}=-2(a_{n+1}-3a_n)\\)\u3092\u78ba\u8a8d\u3059\u308b\u3068\u3001\u6570\u5217\\(\\{a_{n+1}-3a_n\\}\\)\u306f\u521d\u9805\\(a_2-3a_1=1\\)\u3001\u516c\u6bd4\\(-2\\)\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+1}-3a_n=(-2)^{n-1}\\) &#8211; \u2461<\/li>\n<\/ul>\n<p>\\(\u2460-\u2461\\)\u3092\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(5a_n=3^{n-1}-(-2)^{n-1}\\)<\/p>\n<p>\\(a_n=\\displaystyle\\frac{3^{n-1}-(-2)^{n-1}}{5}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u4e00\u822c\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u30662\u3064\u306e\u5f0f\u3092\u4f5c\u3063\u305f\u5f8c\u3001\u305d\u308c\u305e\u308c\u306e\u6f38\u5316\u5f0f\u3092\u4e00\u822c\u9805\u3067\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u306e\u5f8c\u3001\u5f15\u304d\u7b97\u3092\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u6570\u5217\u306e\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u304c\u91cd\u89e3\u306e\u5834\u5408\u306e\u89e3\u304d\u65b9<\/h3>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u91cd\u89e3\u3092\u5f97\u3089\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u4e8c\u6b21\u65b9\u7a0b\u5f0f\\(px^2+qx+r=0\\)\u306e\u89e3\u3092\u03b1\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+2}-\u03b1a_{n+1}=\u03b1(a_{n+1}-\u03b1a_n)\\)<\/li>\n<\/ul>\n<p>\u91cd\u89e3\u3067\u3042\u308b\u305f\u3081\u3001\\(\u03b1=\u03b2\\)\u3067\u3059\u3002\u03b2\u3092\u03b1\u306b\u5909\u3048\u308c\u3070\u3044\u3044\u3060\u3051\u306a\u306e\u3067\u65b0\u305f\u306a\u516c\u5f0f\u3092\u899a\u3048\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u307e\u305f\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3078\u5909\u5f62\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\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>\\(a_1=1\\)\u3001\\(a_2=2\\)\u3001\\(a_{n+2}+6a_{n+1}+9a_n=0\\)\u306b\u3088\u3063\u3066\u5b9a\u3081\u3089\u308c\u308b\u6570\u5217\\(\\{a_n\\}\\)\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(x^2+6x+9=0\\)<\/p>\n<p>\\((x+3)^2=0\\)<\/p>\n<p>\\(x=-3\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u6f38\u5316\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+2}+3a_{n+1}=-3(a_{n+1}+3a_n)\\)<\/li>\n<\/ul>\n<p>\u6570\u5217\\(\\{a_{n+1}+3a_n\\}\\)\u306f\u521d\u9805\\(a_2+3a_1=5\\)\u3001\u516c\u6bd4\\(-3\\)\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+1}+3a_n=5\u00b7(-3)^{n-1}\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3078\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3053\u306e\u6f38\u5316\u5f0f\u3092\u5229\u7528\u3057\u3066\u4e00\u822c\u9805\u3092\u5f97\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002\\(a_{n+1}=pa_n+q^n\\)\u306e\u3088\u3046\u306b\u3001\u6307\u6570\u3092\u542b\u3080\u6f38\u5316\u5f0f\u3067\u306f\u3001\u4e21\u8fba\u3092\u6307\u6570\u3067\u5272\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3067\u304d\u308b\u3068\u3059\u3067\u306b\u5b66\u3093\u3067\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p>\u6f38\u5316\u5f0f\u306f\u8a08\u7b97\u65b9\u6cd5\u304c\u6c7a\u307e\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u3053\u3046\u3057\u305f\u8a08\u7b97\u65b9\u6cd5\u3092\u899a\u3048\u3066\u3044\u306a\u3044\u3068\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u5148\u307b\u3069\u306e\u5f0f\u3067\u3042\u308c\u3070\u3001\u5f0f\u306b\\((-3)^{n-1}\\)\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4e21\u8fba\u3092\\((-3)^{n+1}\\)\u3067\u5272\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{a_{n+1}}{(-3)^{n+1}}+\\displaystyle\\frac{3a_n}{(-3)^{n+1}}=\\displaystyle\\frac{5\u00b7(-3)^{n-1}}{(-3)^{n+1}}\\)<\/p>\n<p>\\(\\displaystyle\\frac{a_{n+1}}{(-3)^{n+1}}+\\displaystyle\\frac{3a_n}{-3\u00b7(-3)^n}\\)\\(=\\displaystyle\\frac{5\u00b7(-3)^{n-1}}{(-3)^2\u00b7(-3)^{n-1}}\\)<\/p>\n<p>\\(\\displaystyle\\frac{a_{n+1}}{(-3)^{n+1}}-\\displaystyle\\frac{a_n}{(-3)^n}=\\displaystyle\\frac{5}{9}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u6570\u5217\\(\\left\\{\\displaystyle\\frac{a_n}{(-3)^n}\\right\\}\\)\u306f\u521d\u9805\\(\\displaystyle\\frac{a_1}{(-3)^1}=-\\displaystyle\\frac{1}{3}\\)\u3001\u516c\u5dee\\(\\displaystyle\\frac{5}{9}\\)\u306e\u7b49\u5dee\u6570\u5217\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{a_n}{(-3)^n}=-\\displaystyle\\frac{1}{3}+(n-1)\\displaystyle\\frac{5}{9}\\)<\/p>\n<p>\\(\\displaystyle\\frac{a_n}{(-3)^n}=\\displaystyle\\frac{5n-8}{9}\\)<\/p>\n<p>\\(a_n=\\displaystyle\\frac{5n-8}{9}\u00b7(-3)^n\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u4e00\u822c\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u3082\u3064\u5834\u5408\u3001\u7b49\u5dee\u6570\u5217\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u7b49\u5dee\u6570\u5217\u3092\u5f97\u305f\u5f8c\u3001\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306f\u8a08\u7b97\u65b9\u6cd5\u304c\u6c7a\u307e\u3063\u3066\u3044\u308b<\/h2>\n<p>\u6f38\u5316\u5f0f\u306f\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u89e3\u304d\u65b9\u3092\u899a\u3048\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3082\u540c\u69d8\u3067\u3059\u3002<\/p>\n<p>\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u5fc5\u305a\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u3088\u3063\u3066\u4e00\u822c\u9805\u306e\u8a08\u7b97\u65b9\u6cd5\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u899a\u3048\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u89e3\u306b1\u3092\u542b\u3080\u5834\u5408\u3001\u968e\u5dee\u6570\u5217\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u307e\u305f\u89e3\u306b1\u3092\u542b\u307e\u306a\u3044\u5834\u5408\u30012\u3064\u306e\u6f38\u5316\u5f0f\u3092\u5229\u7528\u3057\u3066\u5f15\u304d\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002\u91cd\u89e3\u306e\u5834\u5408\u3001\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3092\u4f5c\u3063\u305f\u5f8c\u3001\u4e21\u8fba\u3092\u6307\u6570\u3067\u5272\u308a\u307e\u3059\u3002<\/p>\n<p>\u89e3\u304d\u65b9\u3092\u77e5\u3063\u3066\u3044\u308c\u3070\u3001\u96a3\u63a53\u9805\u9593\u306e\u6f38\u5316\u5f0f\u306e\u8a08\u7b97\u306f\u7c21\u5358\u3067\u3059\u3002\u4e00\u65b9\u3001\u89e3\u304d\u65b9\u3092\u77e5\u3089\u306a\u3051\u308c\u3070\u7b54\u3048\u3092\u5f97\u308b\u306e\u304c\u96e3\u3057\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4e8b\u524d\u306b\u89e3\u304d\u65b9\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6f38\u5316\u5f0f\u3067\u306f\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u79c1\u305f\u3061\u304c\u5b66\u3076\u7279\u6b8a\u306a\u6f38\u5316\u5f0f\u3068\u3057\u3066\u3001\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002 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