Page 200 - Demo

194VargjetAFT%u00cbSI9.3 Vargje t%u00eb ve%u00e7antaNumrat katror%u00eb 1, 4, 9, 16, 25, %u2026Numrat kubik%u00eb1, 8, 27, 64, 125, %u2026Numrat trek%u00ebndor%u00eb1, 3, 6, 10, 15, %u2026Numrat katror%u00eb, kubik%u00eb dhe trek%u00ebndor%u00eb, shoq%u00ebrohen me modele gjeometrike.Progresione aritmetike jan%u00eb vargjet lineare; ato e kan%u00eb ndryshes%u00ebn e %u00e7do kufize me kufiz%u00ebn paraardh%u00ebse nj%u00eb num%u00ebr konstant: T(n + 1) %u2212 T(n) = dProgresionet gjeometrike e kan%u00eb raportin e %u00e7do kufize me kufiz%u00ebn paraardh%u00ebse nj%u00eb num%u00ebr konstant: T(n + 1) : T(n) = rN%u00eb nj%u00eb varg Fibona%u00e7i, %u00e7do kufiz%u00eb p%u00ebrcaktohet si shum%u00eb e dy kufizave paraardh%u00ebse.T(n + 2) = T(n + 1) + T(n) 1, 1, 2, 3, 5, 8, %u2026 2 = 1 + 1, 3 = 2 + 1 etj.T(n + 2) = 3T(n + 1) %u2212 T(n) 1, 1, 2, 5, 13, 34, %u2026 2 = 3 %u00d7 1 %u2212 1, 5 = 2 %u00d7 3 %u2212 1 etj.N%u00eb vargun kuadratik, ndryshesa nd%u00ebrmjet kufizave formon nj%u00eb progresion aritmetik; ndryshesat e radh%u00ebs s%u00eb dyt%u00eb jan%u00eb nj%u00eb num%u00ebr konstant.SHEMBULLa Gjeni nj%u00eb num%u00ebr katror q%u00eb %u00ebsht%u00eb edhe: i num%u00ebr trek%u00ebndor; ii num%u00ebr kubik. b Tregoni q%u00eb secili prej numrave 33, 34 dhe 35 mund t%u00eb shkruhet si shum%u00eb e jo m%u00eb shum%u00eb se tre numrave trek%u00ebndor%u00eb.Renditni: numrat katror%u00eb 1, 4, 9, 16, 25, 36, 49, 64, %u2026numrat trek%u00ebndor%u00eb 1, 3, 6, 10, 15, 21, 28, 36, %u2026numrat kubik%u00eb 1, 8, 27, 64, 125, 216, %u2026a i 1 ose 36 ii 1 ose 64 K%u00ebrkoni numra q%u00eb jan%u00eb n%u00eb t%u00eb dyja listat.b 33 = 21 + 6 + 6 34 = 21 + 10 + 3 35 = 28 + 6 + 1ose 15 + 15 + 3 ose 28 + 6 ose 15 + 10 + 10SHEMBULLN%u00eb vargjet e m%u00ebposhtme, dalloni n%u00ebse progresioni %u00ebsht%u00eb aritmetik apo gjeometrik.a 5, 8, 11, 14, %u2026 b 1, %u22122, 4, %u22128, %u2026 c 3, 3 3, 9, 9 3, %u2026 d 7, 3, %u22121, %u22125, %u2026a 8 %u2013 5 = 11 %u2013 8 = 14 %u2013 11 = 3 b %u20132 : 1 = 4 : %u20132 = %u20138 : 4 = %u20132Aritmetik Ndryshesa konstante: +3 Gjeometrik Her%u00ebsi konstant: %u22122c 3 3 : 3 = 9 : 3 3 = 9 3 : 9 = 3 d 3 %u2013 7 = %u20131 %u2013 3 = %u20135 %u2013 (%u20131) = %u20134Gjeometrik Her%u00ebsi konstant: 3 Aritmetik Ndryshesa konstante: %u22124SHEMBULLGjeni kufizat q%u00eb mungojn%u00eb n%u00eb vargun kuadratik:2, 6, 12, 20, %u25a1, 42, %u25a12 6 12 20 42468 ???22???Progresion aritmetik: 4, 6, 8, 10, 12, 14Kufizat q%u00eb mungojn%u00eb : 20 + 10 = 30 dhe 42 + 14 = 56Progresion aritmetikNdryshesa konstante: +2Kontrolli: 30 + 12 = 42