{"id":4679,"date":"2022-09-01T12:02:19","date_gmt":"2022-09-01T10:02:19","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/aritmeticka-posloupnost-priklad-1\/"},"modified":"2022-09-01T12:02:19","modified_gmt":"2022-09-01T10:02:19","slug":"aritmeticka-posloupnost-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/aritmeticka-posloupnost-priklad-1\/","title":{"rendered":"Aritmetick\u00e1 posloupnost &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Aritmetick\u00e1 posloupnost m\u00e1 n\u00e1sleduj\u00edc\u00ed prvn\u00ed \u010dlen:&nbsp;<strong><em>a1 = 2<\/em><\/strong>. V posloupnosti plat\u00ed, \u017ee dvojn\u00e1sobek sou\u010dtu 2. a 3. \u010dlenu t\u00e9to posloupnosti se rovn\u00e1 trojn\u00e1sobku 4. \u010dlenu t\u00e9to posloupnosti.<\/p>\n<p><strong>Do kter\u00e9ho intervalu pat\u0159\u00ed diference t\u00e9to posloupnosti?<\/strong><br \/>a) \u2329-1,5+ -0,5\u232a<br \/>b) (-0,5; 0,5\u232a<br \/>c) (0,5; 1,5\u232a<br \/>d) (1,5; 2,5\u232a<br \/>e) Takov\u00e1 posloupnost neexistuje.<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>1) Zopakujeme si jak\u00fd je prvn\u00ed \u010dlen aritmetick\u00e9 posloupnosti:<br \/>$$a_{1} = 2$$<br \/>2) Uprav\u00edme si dle zad\u00e1n\u00ed:<br \/>$$2(a_{2}+a_{3})=3a_{4}$$<br \/>3) Rozep\u00ed\u0161eme si spole\u010dn\u011b s diferenci\u00e1ly:<br \/>$$2(a_{1}+d+a_{1}+2d) = 3(a_{1}+3d)$$<br \/>4) Dosad\u00edme si za prvn\u00edho \u010dlena \u010d\u00edslo, viz 1):<br \/>$$2 (2+d+2+2d) = 3 (2 + 3d)$$<br \/>5) Nyn\u00ed se zbav\u00edme z\u00e1vorek:<br \/>$$8 + 6d = 6 + 9d$$<br \/>6) P\u0159evedeme diferenci\u00e1l na jednu stranu a \u010di na druhou:<br \/>$$3d = 2$$<br \/>7) P\u0159epo\u010d\u00edt\u00e1me na 1 diferenci\u00e1l:<br \/>$$d = \\frac{2}{3}$$<br \/><strong>Nyn\u00ed lze ov\u011b\u0159it, \u017ee spr\u00e1vn\u00e1 odpov\u011b\u010f je (c), kdy\u017e si zlomek p\u0159evedeme na desetinn\u00e9 \u010d\u00edslo.<\/strong><\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 6-7 minut <\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4679","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Aritmetick\u00e1 posloupnost - p\u0159\u00edklad 1 | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/aritmeticka-posloupnost-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Aritmetick\u00e1 posloupnost - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Aritmetick\u00e1 posloupnost m\u00e1 n\u00e1sleduj\u00edc\u00ed prvn\u00ed \u010dlen:&nbsp;a1 = 2. V posloupnosti plat\u00ed, \u017ee dvojn\u00e1sobek sou\u010dtu 2. a 3. \u010dlenu t\u00e9to posloupnosti se rovn\u00e1 trojn\u00e1sobku 4. \u010dlenu t\u00e9to posloupnosti. Do kter\u00e9ho intervalu pat\u0159\u00ed diference t\u00e9to posloupnosti?a) \u2329-1,5+ -0,5\u232ab) (-0,5; 0,5\u232ac) (0,5; 1,5\u232ad) (1,5; 2,5\u232ae) Takov\u00e1 posloupnost neexistuje. \u0158e\u0161en\u00ed: 1) Zopakujeme si jak\u00fd je prvn\u00ed \u010dlen aritmetick\u00e9 ... 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V posloupnosti plat\u00ed, \u017ee dvojn\u00e1sobek sou\u010dtu 2. a 3. \u010dlenu t\u00e9to posloupnosti se rovn\u00e1 trojn\u00e1sobku 4. \u010dlenu t\u00e9to posloupnosti. Do kter\u00e9ho intervalu pat\u0159\u00ed diference t\u00e9to posloupnosti?a) \u2329-1,5+ -0,5\u232ab) (-0,5; 0,5\u232ac) (0,5; 1,5\u232ad) (1,5; 2,5\u232ae) Takov\u00e1 posloupnost neexistuje. \u0158e\u0161en\u00ed: 1) Zopakujeme si jak\u00fd je prvn\u00ed \u010dlen aritmetick\u00e9 ... 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