{"id":1080,"date":"2023-08-11T13:27:38","date_gmt":"2023-08-11T10:27:38","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=1080"},"modified":"2025-09-04T17:43:41","modified_gmt":"2025-09-04T14:43:41","slug":"%d0%b1%d0%b0%d0%b3%d1%80%d1%83%d1%82-5-%d0%b7%d0%b8%d0%bc%d0%b0-2023-%d0%b2%d0%b0%d1%80%d0%b8%d0%b0%d0%bd%d1%82-35571-%d0%b7%d0%b0%d0%b4%d0%b0%d0%bd%d0%b8%d0%b5-1%d7%90","status":"publish","type":"post","link":"https:\/\/bagrut-ru.com\/?p=1080","title":{"rendered":"\u0411\u0410\u0413\u0420\u0423\u0422 (5). \u0417\u0418\u041c\u0410 2023, \u0412\u0410\u0420\u0418\u0410\u041d\u0422 35571, \u0417\u0410\u0414\u0410\u041d\u0418\u0415 1\u05d0"},"content":{"rendered":"\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"349\" data-id=\"1084\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/99-1024x349.png\" alt=\"\" class=\"wp-image-1084\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/99-1024x349.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/99-300x102.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/99-768x261.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/99.png 1422w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"351\" data-id=\"1085\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/100-1024x351.png\" alt=\"\" class=\"wp-image-1085\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/100-1024x351.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/100-300x103.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/100-768x263.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/100.png 1436w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/meyda.education.gov.il\/sheeloney_bagrut\/2023\/1\/RUS\/35571.pdf\" data-type=\"link\" data-id=\"https:\/\/meyda.education.gov.il\/sheeloney_bagrut\/2023\/1\/RUS\/35571.pdf\">\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/a><\/p>\n\n\n<div class=\"spoiler-wrap\">\n\t\t\t\t<div class=\"spoiler-head folded\">\u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/div>\n\t\t\t\t<div class=\"spoiler-body\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d0)(1) <\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0431\u043e\u0437\u043d\u0430\u0447\u0438\u043c \\(A(n) \\) \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u044c \\(n\\)-\u0439 \u0447\u043b\u0435\u043d \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0440\u0430\u0432\u0435\u043d \\((3n-2)\\cdot (5n-3)\\),   \u0441\u0443\u043c\u043c\u0430 \\(n\\) \u0447\u043b\u0435\u043d\u043e\u0432 \u044d\u0442\u043e\u0439 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \u0440\u0430\u0432\u043d\u0430  \\(S_n=1\\cdot 2+4\\cdot 7+7\\cdot 12+&#8230;+(3n-2)\\cdot (5n-3)=n(5n^2-2n-1)\\) <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(*)<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435  \\(7\\cdot 12 +10\\cdot 17+&#8230;+58\\cdot 97\\) \u043c\u043e\u0436\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044c \u043a\u0430\u043a \u0441\u0443\u043c\u043c\u0443 \u0447\u0430\u0441\u0442\u0438 \u0447\u043b\u0435\u043d\u043e\u0432 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \\(A(n)\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \\(7\\cdot 12\\) &#8212; \u044d\u0442\u043e \u0442\u0440\u0435\u0442\u0438\u0439 \u0447\u043b\u0435\u043d \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \\(A(n)\\): \\(3\\cdot 3-2=7,\\ 5\\cdot 3-3=12\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \\(10\\cdot 17\\) &#8212; \u044d\u0442\u043e \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u044b\u0439 \u0447\u043b\u0435\u043d \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \\(A(n)\\): \\(3\\cdot 4-2=10,\\ 5\\cdot 4-3=17\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430\u0439\u0434\u0435\u043c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \\(58\\cdot 97\\) \u0447\u043b\u0435\u043d\u043e\u043c \u044d\u0442\u043e\u0439 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438, \u0438 \u0435\u0441\u043b\u0438 \u0434\u0430, \u043a\u0430\u043a\u043e\u0439 \u0435\u0433\u043e \u043d\u043e\u043c\u0435\u0440. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0440\u0435\u0448\u0438\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\( \\Bigg \\{ \\begin {matrix} {3n-2=58}\\\\{5n-3=97}\\end {matrix}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(n=20\\) \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0438 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442 \u0432\u0442\u043e\u0440\u043e\u043c\u0443. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0433\u0434\u0430,   \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0443 <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(*)<\/mark>, \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(7\\cdot 12 +10\\cdot 17+&#8230;+58\\cdot 97=S_{20}-(1\\cdot 2+4\\cdot 7)=20(5\\cdot 20^2-2\\cdot 20-1)-30=39\\ 150\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em> \\(39\\ 150\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(2)<\/mark><\/strong> \u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u0441\u0443\u043c\u043c\u0430 \\(1\\cdot 2+4\\cdot 7+7\\cdot 12+&#8230;+(3n-2)\\cdot (5n-3)+(3n+1)(5n+2)\\) \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u0441\u0443\u043c\u043c\u044b  \\(S_n=1\\cdot 2+4\\cdot 7+7\\cdot 12+&#8230;+(3n-2)\\cdot (5n-3)=n(5n^2-2n-1)\\)  \u043d\u0430\u043b\u0438\u0447\u0438\u0435\u043c \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0433\u043e  \\((3n+1)(5n+2)=(3(n+1)-2)(5(n+1)-3)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0430\u043a \u043a\u0430\u043a \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \\(S_n=1\\cdot 2+4\\cdot 7+7\\cdot 12+&#8230;+(3n-2)\\cdot (5n-3)=n(5n^2-2n-1)\\) \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \\(n\\), \u043e\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c\u0441\u044f \u0438 \u0434\u043b\u044f \\(n+1\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(S_{n+1}=1\\cdot 2+4\\cdot 7+7\\cdot 12+&#8230;+(3n-2)\\cdot (5n-3)+(3(n+1)-2)(5(n+1)-3)=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=1\\cdot 2+4\\cdot 7+7\\cdot 12+&#8230;+(3n-2)\\cdot (5n-3)+(3n+1)(5n+2)=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=(n+1)(5(n+1)^2-2(n+1)-1)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\((n+1)(5(n+1)^2-2(n+1)-1)=(n+1)(5(n^2+2n+1)-2n-2-1)=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\\(=(n+1)(5n^2+8n+2)\\)<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e \\(1\\cdot 2+4\\cdot 7+7\\cdot 12+&#8230;+(3n-2)\\cdot (5n-3)+(3n+1)(5n+2)=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\\(=(n+1)(5n^2+8n+C)\\)<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0433\u0434\u0430 \\((n+1)(5n^2+8n+C)=(n+1)(5n^2+8n+2)\\). \u041e\u0442\u0441\u044e\u0434\u0430 \\(C=2\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em> \u041e\u0442\u0432\u0435\u0442:<\/em> \\(C=2\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div>\n\t\t\t<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-1080","post","type-post","status-publish","format-standard","hentry","category-5"],"_links":{"self":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1080","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1080"}],"version-history":[{"count":15,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1080\/revisions"}],"predecessor-version":[{"id":1318,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1080\/revisions\/1318"}],"wp:attachment":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1080"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1080"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1080"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}