{"id":39,"date":"2022-05-12T10:52:38","date_gmt":"2022-05-12T02:52:38","guid":{"rendered":"https:\/\/www.daixiaomao.com\/bkw\/?p=39"},"modified":"2022-06-08T14:11:10","modified_gmt":"2022-06-08T06:11:10","slug":"bkwdcslsxwt","status":"publish","type":"post","link":"https:\/\/www.daixiaomao.com\/bkw\/39.html","title":{"rendered":"\u7b49\u5dee\u6570\u5217\uff08\u6570\u5b66\u95ee\u9898\uff09"},"content":{"rendered":"\n

\u258c<\/mark><\/strong><\/strong>\u7b80\u4ecb<\/strong><\/p>\n\n\n\n

\u7b49\u5dee\u6570\u5217\u662f\u6307\u4ece\u7b2c\u4e8c\u9879\u8d77\uff0c\u6bcf\u4e00\u9879\u4e0e\u5b83\u7684\u524d\u4e00\u9879\u7684\u5dee\u7b49\u4e8e\u540c\u4e00\u4e2a\u5e38\u6570\u7684\u4e00\u79cd\u6570\u5217\uff0c\u901a\u5e38\u7528A\u3001P\u8868\u793a\u3002\u8fd9\u4e2a\u5e38\u6570\u53eb\u505a\u7b49\u5dee\u6570\u5217\u7684\u516c\u5dee\uff0c\u516c\u5dee\u5e38\u7528\u5b57\u6bcdd\u8868\u793a\u3002<\/p>\n\n\n\n

\u4f8b\u5982\uff1a1,3,5,7,9\u2026\u20262n-1\u3002\u901a\u9879\u516c\u5f0f\u4e3a\uff1aan=a\u2081+(n-1)d\u3002\u9996\u9879a\u2081=1\uff0c\u516c\u5deed=2\u3002\u524dn\u9879\u548c\u516c\u5f0f\u4e3a\uff1aS\u2099=a\u2081n+[n(n-1)d]\/2\u6216Sn=[n*(a\u2081+a\u2099)]\/2\u3002\u6ce8\u610f\uff1a\u4ee5\u4e0an\u5747\u5c5e\u4e8e\u6b63\u6574\u6570\u3002<\/p>\n\n\n\n

\u4e2d\u6587\u540d<\/strong><\/td>\u7b49\u5dee\u6570\u5217<\/td>\u5173\u952e\u8981\u70b9<\/strong><\/td>\u516c\u5dee\u3001\u7b49\u5dee\u4e2d\u9879<\/td><\/tr>
\u5916\u6587\u540d<\/strong><\/td>Arithmetic progression<\/td>\u901a\u9879\u516c\u5f0f<\/strong><\/td>a\u2099=a\u2081+(n-1)d<\/td><\/tr>
\u5b66\u79d1<\/strong><\/td>\u6570\u5b66<\/td>\u6570\u5217\u548c\u516c\u5f0f<\/strong><\/td>S\u2099=(a\u2081+a\u2099)n\u00f72<\/td><\/tr>
\u9879\u6570\u516c\u5f0f<\/strong><\/td>n=(a\u2099-a\u2081)\u00f7d+1<\/td>\u516c\u5dee\u516c\u5f0f<\/strong><\/td>d=(a\u2099-a\u2081)\u00f7(n-1)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

\u258c<\/mark><\/strong><\/strong>\u6027\u8d28<\/strong><\/p>\n\n\n\n

\u5982\u679c\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u7684\u9996\u9879\u8bb0\u4f5ca\uff0c\u516c\u5dee\u8bb0\u4f5cd\uff0c\u90a3\u4e48\u8be5\u7b49\u5dee\u6570\u5217\u7b2c n \u9879 a\u2099\u7684\u4e00\u822c\u9879\u4e3a\uff1a<\/p>\n\n\n\n

an=a+(n-1)d<\/p>\n\n\n\n

\u6362\u53e5\u8bdd\u8bf4\uff0c\u4efb\u610f\u4e00\u4e2a\u7b49\u5dee\u6570\u5217 {a\u2099} \u90fd\u53ef\u4ee5\u5199\u6210\uff1a<\/p>\n\n\n\n

{a\uff0ca+d\uff0ca+2d\uff0c\u00b7\u00b7\u00b7\uff0ca+(n-1)d}<\/p>\n\n\n\n

\u5728\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u4e2d\uff0c\u7ed9\u5b9a\u4efb\u610f\u4e24\u76f8\u8fde\u9879a\u2099\u208a\u2081 \u548c a\u2099 \uff0c\u53ef\u77e5\u516c\u5dee<\/p>\n\n\n\n

d=a\u2099\u208a\u2081-a\u2099<\/p>\n\n\n\n

\u7ed9\u5b9a\u4efb\u610f\u4e24\u9879am\u548can\uff0c\u5219\u516c\u5dee\u662f\uff1a<\/p>\n\n\n\n

d=(a\u2098-a\u2099)\u00f7(m-n)<\/p>\n\n\n\n

\u6b64\u5916\uff0c\u5728\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u4e2d\uff0c\u9009\u53d6\u67d0\u4e00\u9879\uff0c\u8be5\u9879\u7684\u524d\u4e00\u9879\u4e0e\u540e\u4e00\u9879\u4e4b\u548c\uff0c\u4e3a\u539f\u6765\u8be5\u9879\u7684\u4e24\u500d\u3002\u4e3e\u4f8b\u6765\u8bf4\uff0ca\u2081 + a\u2083 = 2a\u2082 \u66f4\u4e00\u822c\u5730\u8bf4\uff0c\u6709\uff1a<\/p>\n\n\n\n

a\u2099\u208b\u2081+a\u2099\u208a\u2081=2a\u2099<\/p>\n\n\n\n

\u8bc1\u660e\u5982\u4e0b\uff1a<\/p>\n\n\n\n

a\u2099\u208b\u2081+a\u2099\u208a\u2081=[a+(n-2)d]+(a+nd)<\/p>\n\n\n\n

=2a+(2n-2)d<\/p>\n\n\n\n

=2[a+(n-1)d]<\/p>\n\n\n\n

=2a\u2099<\/p>\n\n\n\n

\u4ece\u53e6\u4e00\u4e2a\u89d2\u5ea6\u770b\uff0c\u7b49\u5dee\u6570\u5217\u4e2d\u7684\u4efb\u610f\u4e00\u9879\uff0c\u662f\u5176\u524d\u4e00\u9879\u548c\u540e\u4e00\u9879\u7684\u7b97\u672f\u5e73\u5747\uff1a<\/p>\n\n\n\n

a\u2099=(a\u2099\u208b\u2081+a\u2099\u208a\u2081)\u00f72<\/p>\n\n\n\n

\u258c<\/mark><\/strong><\/strong>\u7b49\u5dee\u7ea7\u6570\u548c<\/strong><\/p>\n\n\n\n

\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u7684\u9996 n \u9879\u4e4b\u548c\uff0c\u79f0\u4e3a\u7b49\u5dee\u6570\u5217\u548c\uff08sum of arithmetic sequence\uff09\u6216\u7b97\u672f\u7ea7\u6570\uff08arithmetic series\uff09\uff0c\u8bb0\u4f5c S\u2099\u3002<\/p>\n\n\n\n

\u4e3e\u4f8b\u6765\u8bf4\uff0c\u7b49\u5dee\u6570\u5217 {1, 3, 5, 7} \u7684\u548c\u662f 1 + 3 + 5 + 7 = 16\u3002<\/p>\n\n\n\n

\u7b49\u5dee\u6570\u5217\u6c42\u548c\u7684\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n

S\u2099=n\u00f72(a+a\u2099)<\/p>\n\n\n\n

=n\/2[2a+(n-1)d]<\/p>\n\n\n\n

=an+d\u00b7n(n-1)\/2<\/p>\n\n\n\n

\u7b49\u5dee\u6570\u5217\u548c\u5728\u4e2d\u6587\u6559\u79d1\u4e66\u4e2d\u5e38\u8868\u8fbe\u4e3a\uff1a\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u7684\u548c\uff0c\u7b49\u4e8e\u5176\u9996\u9879\u4e0e\u672b\u9879\u7684\u548c\uff0c\u4e58\u4ee5\u9879\u6570\u9664\u4ee52\u3002<\/p>\n\n\n\n

\u516c\u5f0f\u8bc1\u660e\u5982\u4e0b\uff1a
\u5c06\u7b49\u5dee\u6570\u5217\u548c\u5199\u4f5c\u4ee5\u4e0b\u4e24\u79cd\u5f62\u5f0f\uff1a<\/p>\n\n\n\n

S\u2099=a+(a+d)+(a+2d)+\u00b7\u00b7\u00b7+[a+(n-2)d]+[a+(n-1)d]<\/p>\n\n\n\n

S\u2099=[a\u2099-(n-1)d]+[a\u2099-(n-2)d]+\u00b7\u00b7\u00b7+\uff08a\u2099-2d)+(a\u2099-d)+a\u2099<\/p>\n\n\n\n

\u5c06\u4e24\u516c\u5f0f\u76f8\u52a0\u6765\u6d88\u6389\u516c\u5dee d\uff0c\u53ef\u5f97\uff1a<\/p>\n\n\n\n

2S\u2099=n(a+a\u2099)<\/p>\n\n\n\n

\u6574\u7406\u53ef\u5f97\u7b2c\u4e00\u79cd\u5f62\u5f0f\u3002<\/p>\n\n\n\n

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\u258c<\/mark><\/strong><\/strong>\u76f8\u5173\u6545\u4e8b<\/strong><\/p>\n\n\n\n

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\u9ad8\u65af1777\u5e744\u670830\u65e5\u751f\u4e8e\u4e0d\u4f26\u745e\u514b\u7684\u4e00\u4e2a\u5de5\u5320\u5bb6\u5ead\uff0c1855\u5e742\u670823\u65e5\u5352\u4e8e\u683c\u4e01\u6839\u3002\u5e7c\u65f6\u5bb6\u5883\u8d2b\u56f0\uff0c\u4f46\u806a\u654f\u5f02\u5e38\uff0c\u53d7\u4e00\u8d35\u65cf\u8d44\u52a9\u624d\u8fdb\u5b66\u6821\u53d7\u6559\u80b2\u30021795\uff5e1798\u5e74\u5728\u683c\u4e01\u6839\u5927\u5b66\u5b66\u4e60,1798\u5e74\u8f6c\u5165\u9ed1\u5c14\u59c6\u65bd\u6cf0\u7279\u5927\u5b66\uff0c\u7fcc\u5e74\u56e0\u8bc1\u660e\u4ee3\u6570\u57fa\u672c\u5b9a\u7406\u83b7\u535a\u58eb\u5b66\u4f4d\u3002\u4ece1807\u5e74\u8d77\u62c5\u4efb\u683c\u4e01\u6839\u5927\u5b66\u6559\u6388\u517c\u683c\u4e01\u6839\u5929\u6587\u53f0\u53f0\u957f\u76f4\u81f3\u901d\u4e16\u3002<\/p>\n\n\n\n

\u9ad8\u65af7\u5c81\u90a3\u5e74\uff0c\u7236\u4eb2\u9001\u4ed6\u8fdb\u4e86\u8036\u5361\u6377\u6797\u5b81\u56fd\u6c11\u5c0f\u5b66\uff0c\u8bfb\u4e66\u4e0d\u4e45\uff0c\u9ad8\u65af\u5728\u6570\u5b66\u4e0a\u5c31\u663e\u9732\u51fa\u4e86\u5e38\u4eba\u96be\u4ee5\u6bd4\u8f83\u7684\u5929\u8d4b\uff0c\u6700\u80fd\u8bc1\u660e\u8fd9\u4e00\u70b9\u7684\u662f\u9ad8\u65af\u5341\u5c81\u90a3\u5e74\uff0c\u6559\u5e08\u5f6a\u7279\u8010\u5c14\u5e03\u7f6e\u4e86\u4e00\u9053\u5f88\u7e41\u6742\u7684\u8ba1\u7b97\u9898\uff0c\u8981\u6c42\u5b66\u751f\u628a1\u5230 100\u7684\u6240\u6709\u6574\u6570\u52a0\u8d77\u6765\uff0c\u6559\u5e08\u521a\u53d9\u8ff0\u5b8c\u9898\u76ee\uff0c\u9ad8\u65af\u5373\u523b\u628a\u5199\u7740\u7b54\u6848\u7684\u5c0f\u77f3\u677f\u4ea4\u4e86\u4e0a\u53bb\u3002\u5f6a\u7279\u8010\u5c14\u8d77\u521d\u5e76\u4e0d\u5728\u610f\u8fd9\u4e00\u4e3e\u52a8\uff0c\u5fc3\u60f3\u8fd9\u4e2a\u5c0f\u5bb6\u4f19\u53c8\u5728\u6363\u4e71\uff0c\u4f46\u5f53\u4ed6\u53d1\u73b0\u5168\u73ed\u552f\u4e00\u6b63\u786e\u7684\u7b54\u6848\u5c5e\u4e8e\u9ad8\u65af\u65f6\uff0c\u624d\u5927\u5403\u4e00\u60ca\u3002\u800c\u66f4\u4f7f\u4eba\u5403\u60ca\u7684\u662f\u9ad8\u65af\u7684\u7b97\u6cd5\uff0c\u4ed6\u53d1\u73b0\uff1a\u7b2c\u4e00\u4e2a\u6570\u52a0\u6700\u540e\u4e00\u4e2a\u6570\u662f101\uff0c\u7b2c\u4e8c\u4e2a\u6570\u52a0\u5012\u6570\u7b2c\u4e8c\u4e2a\u6570\u7684\u548c\u4e5f\u662f101\uff0c\u2026\u2026\u5171\u670950\u5bf9\u8fd9\u6837\u7684\u6570\uff0c\u7528101\u4e58\u4ee550\u5f97\u52305050\u3002\u8fd9\u79cd\u7b97\u6cd5\u662f\u6559\u5e08\u672a\u66fe\u6559\u8fc7\u7684\u8ba1\u7b97\u7b49\u7ea7\u6570\u7684\u65b9\u6cd5\uff0c\u9ad8\u65af\u7684\u624d\u534e\u4f7f\u5f6a\u7279\u8010\u5c14\u5341\u5206\u6fc0\u52a8\uff0c\u4e0b\u8bfe\u540e\u7279\u5730\u5411\u6821\u957f\u6c47\u62a5\uff0c\u5e76\u58f0\u79f0\u81ea\u5df1\u5df2\u7ecf\u6ca1\u6709\u4ec0\u4e48\u53ef\u6559\u9ad8\u65af\u7684\u4e86\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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