Ngale ndlela, izinto ezidityaniswe ngokulandelelana kwamanani zilandela ngokulandelelana, oko kukuthi, i-odolo kwiseti.

Ukwahlula

Amanani alandelelanayo anokugqitywa okanye angenasiphelo, umzekelo:

SF = (2, 4, 6,…, 8)

SYo = (2,4,6,8…)

Qaphela ukuba xa imitya ingapheliyo, iboniswa yi-ellipsis ekugqibeleni. Kukwafanelekile ukukhumbula ukuba izinto ezilandelelanayo ziboniswa ngoonobumba a. Umzekelo:

Into yokuqala: a1 = 2

Into yesi-4: a4 4 = 8

Ixesha lokugqibela ngokulandelelana libizwa ngokuba yi-nth, kwaye limelwe ngun. Kule meko, an Ulandelelwano olugqityiweyo lwangaphambili luya kuba yinto yesi-8.

Ke ngoko, sinokuyimela ngolu hlobo lulandelayo:

SF = (ukuya1el2el3,…, Yenan)

SYo = (ukuya1el2el3eln...)

Umthetho woqeqesho

Umthetho woQeqesho okanye iXesha eliQhelekileyo lisetyenziselwa ukubala naliphi na ixesha ngokulandelelana, kuchazwe ngentetho:

unn = 2n2 - 1

Umthetho wokuphindeka

Umthetho wokuphindeka uvumela ukubala naliphi na ixesha lokulandelelana kwamanani kwizinto zangaphambili:

unn = an-1, ukuyan-2, ... a1

Ukuqhubela phambili kwe-Arithmetic kunye nokuqhubela phambili kwejometri.

Iindidi ezimbini zokulandelelana kwamanani ezisetyenziswa ngokubanzi kwimathematics zi-arithmetic kunye nejometri inkqubela phambili.

Ukuqhubela phambili kwe-Arithmetic (AP) kukulandelelana kwamanani okwenyani amiselwe ngu-r rhoqo (umyinge), ofunyanwa ngokudibanisa phakathi kwenombolo nenye.

Ukuqhubela phambili kwejiyometri (PG) kukulandelelana kwamanani apho umlinganiso ohleliyo (r) umiselwa ngokuphindaphinda into ngequotient (q) okanye umlinganiso wePG.

Ukuqonda ngcono, bona le mizekelo ingezantsi:

I-PA = (4,7,10,13,16, XNUMX, XNUMX, XNUMX, XNUMX… an…) Umlinganiselo ongenasiphelo womlinganiselo (r) 3

I-PG (1, 3, 9, 27, 81, ...), ukonyusa ubudlelwane phakathi kolwalamano (r) 3

Funda ulandelelwano lweFibonacci.

Ukuzilolonga kusonjululwe

Ukuwuqonda ngcono umxholo wokulandelelana kwamanani, landela umthambo osonjululweyo:

1) Ukulandela ipateni yokulandelelana kwamanani, lithini inani elilandelayo ngokuhambelana kwezi ndlela zilandelayo:

a) (1, 3, 5, 7, 9, 11, ...)
b) (0, 2, 4, 6, 8, 10,…)
c) (3, 6, 9, 12, ...)
d) (1, 4, 9, 16,…)
e) (37, 31, 29, 23, 19, 17, ...)