{"id":4766,"date":"2022-09-02T14:11:56","date_gmt":"2022-09-02T12:11:56","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/slovni-ulohy-priklad-2-posloupnosti\/"},"modified":"2022-09-02T14:11:56","modified_gmt":"2022-09-02T12:11:56","slug":"slovni-ulohy-priklad-2-posloupnosti","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/slovni-ulohy-priklad-2-posloupnosti\/","title":{"rendered":"Slovn\u00ed \u00falohy – p\u0159\u00edklad 2 (posloupnosti)"},"content":{"rendered":"

Zad\u00e1n\u00ed:<\/strong><\/p>\n

\"\"<\/p>\n

Obrazce sest\u00e1vaj\u00ed z b\u00edl\u00fdch a tmav\u00fdch \u0161esti\u00faheln\u00edk\u016f uspo\u0159\u00e1dan\u00fdch do sloupc\u016f. Po\u010det \u0161esti\u00faheln\u00edk\u016f ve sloupci stoup\u00e1 (v\u017edy o jeden) z lev\u00e9 i prav\u00e9 strany a\u017e do st\u0159edu.
Ka\u017ed\u00fd obrazec m\u00e1 na za\u010d\u00e1tku i na konci jeden b\u00edl\u00fd \u0161esti\u00faheln\u00edk.
V jednom z dal\u0161\u00edch obrazc\u016f je nejdel\u0161\u00ed sloupec slo\u017een z 59 \u0161esti\u00faheln\u00edk\u016f (nad sebou).
a) Ur\u010dete, jak\u00fd bude po\u010det v\u0161ech tmav\u00fdch sloupc\u016f v tomto obrazci.<\/strong>
b) Ur\u010dete tak\u00e9 po\u010det b\u00edl\u00fdch \u0161esti\u00faheln\u00edk\u016f v obrazci.<\/strong><\/p>\n

\u0158e\u0161en\u00ed:<\/strong><\/p>\n

V obrazci, kde je 59 \u0161esti\u00faheln\u00edk\u016f uprost\u0159ed se jedn\u00e1 o b\u00edl\u00e9 \u0161esti\u00faheln\u00edky uprost\u0159ed
1) Nejd\u0159\u00edve si zrekapitulujeme, co ji\u017e v\u00edme
$$a_{1} = 1$$
$$a_{2} = 2$$
$$d = 2$$
$$a_{n} = 57$$
2) Nyn\u00ed zjist\u00edme, kolik\u00e1t\u00fd je prvek n, podle t\u00e9to rovnice
$$a_{n} = a_{1} + (n-1)2$$
3) Dosad\u00edme, co zn\u00e1me
$$57 = 1 + (n-1)2$$
4) Jedni\u010dku si p\u0159evedeme na levou stranu a na prav\u00e9 stran\u011b rozn\u00e1sob\u00edme z\u00e1vorku 2
$$56 = 2n-2$$
5) \u010c\u00edsla si p\u0159evedeme na jednu stranu a nezn\u00e1m\u00e9 tak\u00e9
$$58 = 2n$$
6) P\u0159epo\u010d\u00edt\u00e1me na 1 n
$$n = 29$$
7) Po\u010det tmav\u00fdch sloupk\u016f je tedy dvojn\u00e1sobkem n (odpov\u011b\u010f na ot\u00e1zku a):<\/strong>
$$29\\cdot 2 = 58$$
8) Po\u010det \u010dlen\u016f vypo\u010d\u00edt\u00e1me podle vzore\u010dku
$$s_{n} = \\frac{n}{2}(a_{1}+a_{n})$$
9) Dosad\u00edme
$$s_{29} = \\frac{29}{2}(1+57)$$
10) Nejd\u0159\u00edve se\u010dteme \u010d\u00edsla v z\u00e1vorce (58), t\u00edmto \u010d\u00edslem vyn\u00e1sob\u00edme \u010ditatele a v\u0161e pak vyd\u011bl\u00edme jmenovatelem (2)
$$s_{29} =841$$
11) Nyn\u00ed m\u016f\u017eeme vypo\u010d\u00edtat po\u010det b\u00edl\u00fdch \u0161esti\u00faheln\u00edku dle tohoto vzore\u010dku
$$x_{B} = 841+59+841$$
12) Po\u010det b\u00edl\u00fdch \u0161esti\u00faheln\u00edk\u016f tedy je (odpov\u011b\u010f na ot\u00e1zku b):<\/strong>
$$x_{B} = 1741 ks$$<\/p>\n

\u010casov\u00e1 n\u00e1ro\u010dnost: 7-8 minut<\/p>\n

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-4766","lesson","type-lesson","status-publish","hentry"],"yoast_head":"\nSlovn\u00ed \u00falohy - p\u0159\u00edklad 2 (posloupnosti) | 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\/slovni-ulohy-priklad-2-posloupnosti\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Slovn\u00ed \u00falohy - p\u0159\u00edklad 2 (posloupnosti) | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Obrazce sest\u00e1vaj\u00ed z b\u00edl\u00fdch a tmav\u00fdch \u0161esti\u00faheln\u00edk\u016f uspo\u0159\u00e1dan\u00fdch do sloupc\u016f. 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