Hanya Mai Sauri Don Magance Matsalolin Jerin
Tambayoyin jeri (jeri na lamba) nau'in tambaya ce da aka saba yi a jarrabawar shiga makaranta, jarrabawar zaɓen aiki, har ma da gwaje-gwajen ƙwarewa na asali. Manufar tana da sauƙi: ana tambayarka ka nemo tsari a cikin jerin lambobi, sannan ka tantance lamba ta gaba (ko lambar da ta ɓace). Duk da cewa suna iya zama kamar rikitarwa, ana iya warware jerin cikin sauri idan kana da "taswirar" matakai bayyanannu. Wannan labarin ya tattauna yadda ake magance matsalolin jeri cikin sauri ta amfani da dabarun aiki, nau'ikan alamu da aka fi sani, da shawarwari don guje wa alamu na ƙarya.
1. Fahimci manufar matsalar jerin
Ainihin, tambayoyin jerin suna gwada ikon ku na gane alaƙar da ke tsakanin lambobi. Waɗannan alaƙar na iya haɗawa da ƙari, ragi, ninkawa, rabawa, haɗuwar ayyuka, har ma da tsare-tsare ko rukunonin da suka dogara da matsayi.
Yawanci tambayoyin suna cikin tsari:
– Kayyade lamba ta gaba: 2, 4, 8, 16, …
– Ka tantance lambobin da suka ɓace: 3, 6, __, 24, 48
– Zaɓi amsar da ta fi dacewa daga zaɓuɓɓukan da ake da su.
Mabuɗin da ya fi sauri shine: kada ku yi zato ba zato ba tsammani. Yi amfani da waɗannan matakan tsari.
2. Matakai masu sauri (hanyar gama gari) don warware jerin
Ga jerin hanyoyin tunani masu inganci waɗanda ake amfani da su a gwaje-gwaje:
1) Duba bambanci (bambanci) tsakanin lambobi
Lissafa bambance-bambancen da ke jere: a2–a1, a3–a2, da sauransu. Jerin abubuwa masu sauƙi da yawa suna amfani da bambance-bambancen da ba sa canzawa (jerin lissafi) ko bambance-bambancen da ke samar da tsari.
2) Duba rabo (rabo)
Idan bambance-bambancen ba su da kyau, gwada rabawa: a2/a1, a3/a2, da sauransu. Wannan yana taimakawa wajen nemo jerin siffofi na geometric ko tsarin ninkawa.
3) Duba tsarin gauraye (matakai biyu/masu canzawa)
Jerin sau da yawa suna amfani da tsari mai canzawa: ƙara, ninka, ƙara, ninka. Ko kuma jere biyu masu canzawa (lambobi marasa kyau suna samar da tsari ɗaya, har ma lambobi suna samar da wani).
4) Duba tsarin mataki na biyu (bambancin bambanci)
Idan bambancin yana canzawa akai-akai, ƙididdige bambancin. Wannan yakan faru ne a cikin jerin quadratic ko tsarin ƙara mataki-mataki.
5) Duba alamu na musamman: murabba'i, cubic, prime, Fibonacci, factorial
Gwaje-gwaje da yawa suna nuna alamu na "alama". Idan lambobin sun yi kama da waɗanda aka saba gani (1, 4, 9, 16...) to wataƙila murabba'i ne.
6) Duba tsarin da aka yi amfani da shi ta hanyar lambobi
Wani lokaci tsarin ba ya cikin ƙimar, amma a cikin lambar: jimlar lambobi, juyawa, ƙara lambobi, ko ninki na 9/11.
Da wannan tsari, ba za ku ɓata lokaci ba. Kawai kuna buƙatar yin aiki da shi har sai ya zama atomatik.
3. Tsarin jerin da aka fi samu akai-akai da kuma hanya mafi sauri ta yin hakan
A. Jerin Lissafi (bambanci mai ɗorewa)
Misali: 5, 9, 13, 17, …
Bambancin: +4, +4, +4.
Sai lamba ta gaba: 21.
Dabara mai sauri: da zarar ka sami bambanci iri ɗaya sau biyu a jere, ci gaba da wannan tsarin.
B. Jerin siffofi na lissafi (rabo mai dorewa)
Misali: 3, 6, 12, 24, …
Rabon: ×2, ×2, ×2.
Na gaba: 48.
Shawara mai sauri: idan lambobin sun ƙaru ko sun ragu da sauri, yi zargin ninkawa/rabawa.
C. Jerin bambancin maki (bambancin da ke ƙaruwa akai-akai)
Misali: 2, 5, 9, 14, 20, …
Bambanci: +3, +4, +5, +6.
Bambanci na gaba +7 → 27.
Shawara mai sauri: idan bambancin ya "haura ɗaya bayan ɗaya", to alama ce ta tsari mai matakai.
D. Jerin 'yan hudu da na cubic
– Murabba'ai: 1, 4, 9, 16, 25, … (n²)
– Cubic: 1, 8, 27, 64, … (n³)
Dabara mai sauri: haddace murabba'ai 1-15 da kuma murabba'ai 1-10. Wannan yana hanzarta gane su da daƙiƙa.
Jerin Fibonacci na E. da bambance-bambancensa
Fibonacci na gargajiya: 1, 1, 2, 3, 5, 8, 13, …
Kowace lamba = jimlar lambobi biyu da suka gabata.
Sau da yawa bambance-bambancen da ke faruwa:
2, 3, 5, 8, 13, 21, … (farawa daga 2 da 3).
Dabara mai sauri: duba ko a(n) = a(n-1) + a(n-2). Idan ya dace da matakai 2-3, yawanci amsar ita ce.
F. Jerin lambobi na farko
2, 3, 5, 7, 11, 13, 17, …
Dabara mai sauri: haddace firam har zuwa 50. Matsaloli da yawa suna tsayawa a cikin wannan kewayon.
Jerin factorial na G.
1, 2, 6, 24, 120, … (1!, 2!, 3!, 4!, 5!)
Dabara mai sauri: duba idan ninkawa sun haɗu: ×2, ×3, ×4, ×5.
H. Tsarin da ke canzawa (ayyuka biyu)
Misali: 2, 6, 7, 21, 22, 66, …
Tsarin: ×3, +1, ×3, +1, ×3 …
Na gaba: 67.
Dabara mai sauri: idan babu tsari ɗaya, gwada raba ayyukan "ninka da ƙara" a madadin.
I. Jerin lambobi guda biyu masu canzawa (lambobi masu ban mamaki da ma suna da tsari daban-daban)
Misali: 1, 4, 2, 8, 3, 12, 4, …
Lambobin matsayi marasa daidaituwa: 1, 2, 3, 4 (ƙara +1)
Lambobin matsayi iri ɗaya: 4, 8, 12 (ƙara +4)
Na gaba (matsayi daidai): 16.
Dabara mai sauri: raba zuwa layuka biyu: (na 1, na 3, na 5,…) da (na 2, na 4, na 6,…).
J. Tsarin da ya dogara da lambobi
Misali: 10, 11, 13, 17, 25, …
Wani lokaci tsarin shine jimlar lambobin, ko kuma "lambar da ke gaba = lambar da ta gabata + jimlar lambobinta".
Misali, ƙa'idar: a(n+1) = a(n) + (jimillar lambobi na a(n)).
Dabara mai sauri: idan lambobin sun yi kama da "abin mamaki" kuma ba su dace da bambancin/rabo ba, duba lambobin.
4. Dabaru don guje wa tarkon zane na ƙarya
A cikin gwaje-gwaje, masu ɗaukar jarabawa galibi suna ba da jerin abubuwan da suka "yi kama" da suka dace da tsare-tsare da yawa. Yadda za a guji wannan:
1) Gwada tsarin akan aƙalla sauyi 3
Kada ka gamsu da wasa ɗaya kawai. Ka tabbata ka haɗa lambobi da yawa.
2) Zaɓi tsari mafi sauƙi kuma mafi daidaito.
Idan akwai hanyoyi guda biyu, yawanci wanda aka zaɓa shine tsarin da ba shi da rikitarwa kuma ya shafi dukkan lambobi.
3) Kula da zaɓuɓɓukan amsa
A cikin tambayoyin da suka shafi zaɓuɓɓuka da yawa, wani lokacin za ka iya gwada ɗaya daga cikin tsare-tsaren sannan ka ga ko sakamakon ya bayyana a cikin zaɓuɓɓukan. Idan ba haka ba, tsarin ba daidai ba ne.
5. Misalai na gajerun ayyuka (hanyar sauri)
1) 7, 14, 28, 56, …
Duba rabo: ×2 sannan → na gaba 112.
2) 3, 8, 15, 24, 35, …
Bambanci: +5, +7, +9, +11 (sama da 2) → na gaba +13 = 48.
3) 1, 3, 6, 10, 15, …
Bambanci: +2, +3, +4, +5 → na gaba +6 = 21 (wannan jerin alwatika ne).
6. Nasihu don koyo cikin sauri
– Yi jerin tsare-tsare da dole ne a haddace: murabba'i, cubic, prime, factorial, Fibonacci.
– Yi tambayoyi 10-20 a kowace rana: ya fi kyau a yi su akai-akai fiye da da yawa amma ba kasafai ake yi ba.
– Yi amfani da agogon gudu: yi nufin daƙiƙa 20-40 a kowace tambaya don matakin farko.
– Ka lura da tsarin da kake yawan zato ba daidai ba: zai zama “kuskure” wanda zai hanzarta ingantawa.
Penutup
Magance matsalolin jerin abubuwa cikin sauri ba wai game da baiwa ba ne, sai dai dabaru da ɗabi'a. Fara da matakai da aka fi sani (bambanci da rabo), ci gaba zuwa tsarin canzawa ko tsaka-tsaki, sannan a duba takamaiman tsari kamar murabba'i, firam, lambobin Fibonacci, ko factorials. Da yawan yin atisaye, za ku saba da gano alamu cikin 'yan daƙiƙa kaɗan. Idan kun daidaita, matsalolin jerin abubuwa da suka zama kamar rikitarwa da farko za su fi sauƙi da sauri a warware su.
Idan kana so, ka aiko min da misalai 5-10 na matsalolin jerin da kake da su, kuma zan taimaka maka ka tattauna su ɗaya bayan ɗaya ta amfani da hanyar da ta fi sauri.
