Page 274 - Demo

268 P%u00ebrgjigjet*12 Dy vargjet mund t%u00eb p%u00ebrmbajn%u00eb t%u00eb nj%u00ebjt%u00ebn kufiz%u00eb n%u00eb pozicione t%u00eb ndryshme.9.2A1 a 2, 3, 6, 11 b 5, 7, 11, 17 c 10, 11, 13, 16 d 5, 8, 14, 23 e 10, 9, 6, 1, f 8, 6, 2, %u221246 a n2 + 3 b n2 %u22124 c 2n2 d n2 + ne n2 + 4n f n2 + 2n g 2n2 + 2n + 2 h 4n %u2212 n28 a Vlerat nd%u00ebrmjet 30 dhe 40 b n2 + nc N%u00eb qoft%u00eb se n2 + n t%u0003%u0014%u0003%u0013%u0013%u0013%u0003at%u00ebher%u00eb n2 + n - %u0014%u0003%u0013%u0013%u0013%u0003t%u0003%u0013. Vlera m%u00eb e vog%u00ebl e n = 32.9 Jo. N%u00eb qoft%u00eb se n2 + 3 %u0010%u0003%u0014%u0018%u0013, at%u00ebher%u00eb n2 - 147. 147 nuk %u00ebsht%u00eb num%u00ebr katror i plot%u00eb, ndaj 150 nuk %u00ebsht%u00eb kufiz%u00eb e vargut.10 Po: 3n2 %u2013 n = n(3n %u2013 1) N%u00ebse n %u00ebsht%u00eb %u00e7ift: 3n %u2013 1 %u00ebsht%u00eb tek, pra %u00e7ift %u00d7 tek = %u00e7ift N%u00ebse n %u00ebsht%u00eb tek: 3n %u2013 1 %u00ebsht%u00eb %u00e7ift, pra tek %u00d7 %u00e7ift = %u00e7ift9.2Z1 Jo, kufiza e 10-t%u00eb nuk %u00ebsht%u00eb dyfishi i kufiz%u00ebs s%u00eb 5-t%u00eb (ose kufiza e 10-t%u00eb = 103).2 a Jo, meq%u00eb ndryshesa e dyt%u00eb = 2, kufiza e n-t%u00eb do t%u00eb filloj%u00eb me %u201cn2\ b n2 - n + 53 T(n) = n2 %u2212 n: 0, 2, 6, 12; T(n) = n2 %u2212 1: 0, 3, 8, 15;T(n) = n2 + 2: 3, 6, 11, 18; T(n) = n(n + 1): 2, 6, 12, 20; T(n) = 4 %u2212 n2: 3, 0, %u22125, %u2212124 Shum%u00eb p%u00ebrgjigje t%u00eb mundshme duke p%u00ebrfshir%u00eb n2+ n + 1, 2n2 %u2212 2n + 3, 12 n2 + 212 n, 3n2 %u2212 5n + 5, 4n2 %u2212 8n + 7 5 ab m = 32 n2 %u2013 32 n + 4c modeli i 10-t%u00eb d 3 679 fije shkrep%u00ebse67 8 3169 a 24 l%u00ebvizje b 15 l%u00ebvizje, 8 l%u00ebvizjec Numri i %u00e7ifteve 1 2 3 4Numri i l%u00ebvizjeve 3 8 15 24d Numri i l%u00ebvizjeve = n2 + 2n ku n = numri i %u00e7ifteve. Numri i l%u00ebvizjeve p%u00ebr 50 %u00e7ifte = 2 600.10 a 1 3 6 10 15 Ndryshesa e par%u00eb 2 3 4 5 Ndryshesa e dyt%u00eb 1 1 1 Ndryshesa e dyt%u00eb %u00ebsht%u00eb 1, ndaj pjesa e par%u00eb e kufiz%u00ebs s%u00eb n-t%u00eb %u00ebsht%u00eb 12 n2. Termi i n-t%u00eb p%u00ebr ndryshes%u00ebn %u00ebsht%u00eb 12 n. Ndaj termi i p%u00ebrgjithsh%u00ebm n %u00ebsht%u00eb: 12 n2 + 12 n = 12 n(n + 1). b %u00c7do term t%u00eb vargut trek%u00ebndor e konsiderojm%u00eb t%u00eb dyfishuar dhe t%u00eb shnd%u00ebrruar n%u00eb nj%u00eb drejtk%u00ebndor. x x xx xxxx xxxxxxx x xxxx xxxxxxxxx xxxxxxxxxx Termi n i vargut mund t%u00eb shnd%u00ebrrohet n%u00eb drejtk%u00ebndor me p%u00ebrmasa n %u00d7 (n + 1). Por ky %u00ebsht%u00eb dyfishi i numrit trek%u00ebndor, pra: numri trek%u00ebndor i n-t%u00eb = 12 n (n + 1).*11a n3 b 2n3 c n3 %u2013 n d n3 %u2013 2n2 + 3n %u2013 49.3A1 a 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 b 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 c 1, 8, 27, 64, 125, 216, 343, 512, 729, 1 0002 a 21 + 3 + 6 b 28 + 3 c 28 + 3 + 13 a progresion aritmetik g varg i Fibona%u00e7it h progresion gjeometrikm progresion gjeometrik o progresion aritmetik 10 b 0, -1, -1, 0, 1 d 1, 1, 1, 1, 111 Po, p%u00ebrdorim rregullin T(1) = 1, T(2) = 3, T(3) = 6, ..., i cili %u00ebsht%u00eb vargu i numrave trek%u00ebndor%u00eb.12 T%u00eb dyja jan%u00eb t%u00eb sakta, numrat katror%u00eb t%u00eb plot%u00eb formojn%u00eb nj%u00eb varg kuadratik.13 a i 12 , 23 , 34 , 45 , 56 ii 12 , 25 , 310, 417, 526iii 1, 14 , 19 , 116, 125 iv 15 , 43 , 94 , 165 , 256