{"common":{"save":0,"post_id":"7049","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"4872","post_id":"7049","mon_id":"1158924","chapter_id":"1159147","question":"<p>M\u1ed9t chi\u1ebfc \u0111\u1ed3ng h\u1ed3 \u0111&aacute;nh chu&ocirc;ng, s\u1ed1 ti\u1ebfng chu&ocirc;ng \u0111\u01b0\u1ee3c \u0111&aacute;nh b\u1eb1ng s\u1ed1 gi\u1edd m&agrave; \u0111\u1ed3ng h\u1ed3&nbsp;ch\u1ec9 t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111&aacute;nh chu&ocirc;ng. H\u1ecfi m\u1ed9t ng&agrave;y \u0111\u1ed3ng h\u1ed3 \u0111&oacute; \u0111&aacute;nh bao nhi&ecirc;u ti\u1ebfng&nbsp;chu&ocirc;ng b&aacute;o gi\u1edd (m\u1ed7i ng&agrave;y 24 ti\u1ebfng)?<\/p>","options":["<strong>A.<\/strong> 120","<strong>B.<\/strong> 78","<strong>C.<\/strong> 156","<strong>D.<\/strong> 24"],"correct":"3","level":"2","hint":"<p>G\u1ecdi&nbsp;<span class=\"math-tex\">$u_n$<\/span>&nbsp;l&agrave; s\u1ed1 ti\u1ebfng chu&ocirc;ng \u1edf gi\u1edd th\u1ee9 n, trong \u0111&oacute;&nbsp;<span class=\"math-tex\">$1\\le n \\le 12$<\/span>. Sau 12 gi\u1edd \u0111\u1ed3ng h\u1ed3 \u0111&aacute;nh \u0111\u01b0\u1ee3c:<\/p><p><span class=\"math-tex\">$S_{12}=u_1+u_2+...+u_{12}=1+2+...+12=6(1+12)= ...$<\/span>&nbsp;(ti\u1ebfng)<\/p><p>....<\/p>","answer":"<p>G\u1ecdi&nbsp;<span class=\"math-tex\">$u_n$<\/span>&nbsp;l&agrave; s\u1ed1 ti\u1ebfng chu&ocirc;ng \u1edf gi\u1edd th\u1ee9 n, trong \u0111&oacute;&nbsp;<span class=\"math-tex\">$1\\le n \\le 12$<\/span>. Sau 12 gi\u1edd \u0111\u1ed3ng h\u1ed3 \u0111&aacute;nh \u0111\u01b0\u1ee3c:<\/p><p><span class=\"math-tex\">$S_{12}=u_1+u_2+...+u_{12}=1+2+...+12=6(1+12)=78$<\/span>&nbsp;(ti\u1ebfng)<\/p><p>M\u1ed9t ng&agrave;y \u0111\u1ed3ng h\u1ed3 \u0111&aacute;nh \u0111\u01b0\u1ee3c 78 . 2 = 156 (ti\u1ebfng).<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;156&nbsp;<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-06 02:41:37","option_type":"txt","len":0},{"id":"4874","post_id":"7049","mon_id":"1158924","chapter_id":"1159147","question":"<p>Tr&ecirc;n m\u1ed9t b&agrave;n c\u1edd c&oacute; nhi\u1ec1u &ocirc; vu&ocirc;ng, ng\u01b0\u1eddi ta \u0111\u1eb7t 7 h\u1ea1t d\u1ebb v&agrave;o &ocirc; \u0111\u1ea7u ti&ecirc;n. Sau \u0111&oacute; \u0111\u1eb7t ti\u1ebfp v&agrave;o &ocirc;&nbsp;th\u1ee9 hai s\u1ed1 h\u1ea1t nhi\u1ec1u h\u01a1n &ocirc; th\u1ee9 nh\u1ea5t l&agrave; 5, ti\u1ebfp t\u1ee5c \u0111\u1eb7t v&agrave;o &ocirc; th\u1ee9 ba s\u1ed1 h\u1ea1t nhi\u1ec1u h\u01a1n &ocirc; th\u1ee9 hai l&agrave;&nbsp;5,&hellip; v&agrave; c\u1ee9 th\u1ebf ti\u1ebfp t\u1ee5c \u0111\u1ebfn &ocirc; th\u1ee9 n. Bi\u1ebft r\u1eb1ng \u0111\u1eb7t h\u1ebft s\u1ed1 &ocirc; tr&ecirc;n b&agrave;n c\u1edd ng\u01b0\u1eddi ta ph\u1ea3i s\u1eed d\u1ee5ng&nbsp;25450 h\u1ea1t. H\u1ecfi b&agrave;n c\u1edd \u0111&oacute; c&oacute; bao nhi&ecirc;u &ocirc; vu&ocirc;ng?<\/p>","options":["<strong>A.<\/strong> 120","<strong>B.<\/strong> 150","<strong>C.<\/strong> 200","<strong>D.<\/strong> 100"],"correct":"4","level":"2","hint":"<p>S\u1ed1 h\u1ea1t d\u1ebb tr&ecirc;n m\u1ed7i &ocirc; (b\u1eaft \u0111\u1ea7u t\u1eeb &ocirc; th\u1ee9 nh\u1ea5t) theo th\u1ee9 t\u1ef1 \u0111&oacute; l\u1eadp th&agrave;nh c\u1ea5p s\u1ed1 c\u1ed9ng&nbsp;<span class=\"math-tex\">$(u_n)$<\/span>&nbsp;c&oacute;&nbsp;<span class=\"math-tex\">$u_1=7;d=5$<\/span>.<\/p>","answer":"<p>S\u1ed1 h\u1ea1t d\u1ebb tr&ecirc;n m\u1ed7i &ocirc; (b\u1eaft \u0111\u1ea7u t\u1eeb &ocirc; th\u1ee9 nh\u1ea5t) theo th\u1ee9 t\u1ef1 \u0111&oacute; l\u1eadp th&agrave;nh c\u1ea5p s\u1ed1 c\u1ed9ng&nbsp;<span class=\"math-tex\">$(u_n)$<\/span>&nbsp;c&oacute;&nbsp;<span class=\"math-tex\">$u_1=7;d=5$<\/span>.<\/p><p>G\u1ecdi n l&agrave;&nbsp;s\u1ed1 &ocirc; tr&ecirc;n b&agrave;n c\u1edd th&igrave;&nbsp;<span class=\"math-tex\">$u_1+u_2+..+u_n=25450=S_n$<\/span><\/p><p>Ta c&oacute;:<\/p><p><span class=\"math-tex\">$S_n=nu_1+\\dfrac{n(n-1)}{2}.d$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow 25450=7n+\\dfrac{n^2-n}{2}.5$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow 5n^2+9n-50900=0$<\/span><\/p><p>Suy ra n = 100<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>D.<\/strong>&nbsp;100<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-06 02:51:22","option_type":"txt","len":0},{"id":"4875","post_id":"7049","mon_id":"1158924","chapter_id":"1159147","question":"<p>Cho&nbsp;<span class=\"math-tex\">$(u_n)$<\/span>&nbsp;l&agrave; c\u1ea5p s\u1ed1 c\u1ed9ng v\u1edbi c&ocirc;ng sai d, s\u1ed1 h\u1ea1ng \u0111\u1ea7u&nbsp;<span class=\"math-tex\">$u_1$<\/span> th\u1ecfa m&atilde;n <span class=\"math-tex\">$\\begin{cases}u_1+2u_2+u_3=28\\\\u_4+u_5=39\\end{cases}$<\/span>. T&iacute;nh&nbsp;t\u1ed5ng 2023 s\u1ed1 h\u1ea1ng \u0111\u1ea7u c\u1ee7a d&atilde;y.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$S_{2023}=10230310$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$S_{2023}=10230311$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$S_{2023}=\\dfrac{20470737}{2}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$S_{2023}=20230311$<\/span>"],"correct":"2","level":"2","hint":"","answer":"<p>Ta c&oacute;:<\/p><p><span class=\"math-tex\">$\\begin{cases}u_1+2u_2+u_3=28\\\\u_4+u_5=39\\end{cases}$<\/span>&nbsp;<span class=\"math-tex\">$\\Leftrightarrow \\begin{cases}u_1+2(u_1+d)+u_1+2d=28\\\\u_1+3d+u_1+4d=39\\end{cases}$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow \\begin{cases}4u_1+4d=28\\\\2u_1+7d=39\\end{cases}$<\/span>&nbsp;<span class=\"math-tex\">$\\Leftrightarrow \\begin{cases}u_1=2\\\\d=5\\end{cases}$<\/span><\/p><p>T\u1ed5ng c\u1ee7a 2023 s\u1ed1 h\u1ea1ng \u0111\u1ea7u l&agrave;:<\/p><p><span class=\"math-tex\">$S_{2023}=2023.2+\\dfrac{2023.2022}{2}.5=10230311$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;<span class=\"math-tex\">$S_{2023}=10230311$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-06 02:54:38","option_type":"math","len":0}]}