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Arifmetik progressiyani takrorlash

Arifmetik progressiyani takrorlang va unga oid masalalarni yeching.

Arifmetik progressiya qismlari va formulalari

Arifmetik progressiyada ketma-ket hadlar orasidagi farq doim bir xildir. Biz uni progressiya ayirmasi deb ataymiz.
Masalan, quyidagi progressiyaning ayirmasi plus, 2 ga teng:
start color #ed5fa6, plus, 2, \curvearrowright, end color #ed5fa6start color #ed5fa6, plus, 2, \curvearrowright, end color #ed5fa6start color #ed5fa6, plus, 2, \curvearrowright, end color #ed5fa6
3, comma5, comma7, comma9, comma, point, point, point
Arifmetik progressiya formulalari yordamida a, left parenthesis, n, right parenthesis va progressiyaning n, start text, negative, end texthadini topishimiz mumkin.
Quyidagi arifmetik progressiyaning oshkor formulasidir. Bunda birinchi had start color #11accd, k, end color #11accd va progressiya ayirmasi start color #ed5fa6, d, end color #ed5fa6 ga teng.
a, left parenthesis, n, right parenthesis, equals, start color #11accd, k, end color #11accd, plus, left parenthesis, n, minus, 1, right parenthesis, start color #ed5fa6, d, end color #ed5fa6
Bu yuqoridagi progressiyaning rekursiv formulasi:
{a(1)=ka(n)=a(n1)+d\begin{cases}a(1) = \blueD k \\\\ a(n) = a(n-1)+\maroonC d \end{cases}
Arifmetik progressiya haqida koʻproq maʼlumotga ega boʻlmoqchimisiz? Unda ushbu videoni koʻring.

Arifmetik progressiyani kengaytirish

3, comma, 8, comma, 13, comma, point, point, point progressiyani kengaytirishimiz kerak boʻlsin. Koʻrinib turibdiki, har bir had oldingisidan start color #ed5fa6, plus, 5, end color #ed5fa6 ga farq qiladi:
start color #ed5fa6, plus, 5, \curvearrowright, end color #ed5fa6start color #ed5fa6, plus, 5, \curvearrowright, end color #ed5fa6start color #ed5fa6, plus, 5, \curvearrowright, end color #ed5fa6
3, comma8, comma13, comma, point, point, point
Keyingi hadni topish uchun qoʻshishimiz kerak boʻlgan farq 18 ga teng:
start color #ed5fa6, plus, 5, \curvearrowright, end color #ed5fa6start color #ed5fa6, plus, 5, \curvearrowright, end color #ed5fa6start color #ed5fa6, plus, 5, \curvearrowright, end color #ed5fa6
3, comma8, comma13, comma18, comma, point, point, point
1-masala
  • Joriy
minus, 5, comma, minus, 1, comma, 3, comma, 7, comma, dots progressiyaning keyingi hadi nechaga teng?
  • Javobingiz quyidagicha boʻlishi kerak:
  • 6 kabi butun son
  • 3, slash, 5 kabi soddalashtirilga toʻgʻri kasr
  • 7, slash, 4 kabi soddalashtirilgan notoʻgʻri kasr
  • 1, space, 3, slash, 4 kabi aralash son
  • 0, point, 75 kabi aniq oʻnli kasr
  • 12, space, start text, p, i, end text yoki 2, slash, 3, space, start text, p, i, end text kabi pi ning karralisi

Shunga oʻxshash masalalarni yechmoqchimisiz? Ushbu mashqni koʻring.

Rekursiv formulani yozish

3, comma, 8, comma, 13, comma, point, point, pointning rekursiv formulasini yozishimiz kerak boʻlsin. Biz bilamizki, progressiya ayirmasi start color #ed5fa6, plus, 5, end color #ed5fa6 ga teng. Bundan tashqari, birinchi had start color #11accd, 3, end color #11accd ga teng. Demak, bu quyidagi progressiya uchun rekursiv formuladir:
{a(1)=3a(n)=a(n1)+5\begin{cases}a(1) = \blueD 3 \\\\ a(n) = a(n-1)\maroonC{+5} \end{cases}
1-masala
  • Joriy
minus, 5, comma, minus, 1, comma, 3, comma, 7, comma, dots progressiya uchun rekursiv formuladagi k va d ni toping.
{a(1)=ka(n)=a(n1)+d\begin{cases}a(1) = k \\\\ a(n) = a(n-1)+d \end{cases}
k, equals
  • Javobingiz quyidagicha boʻlishi kerak:
  • 6 kabi butun son
  • 3, slash, 5 kabi soddalashtirilga toʻgʻri kasr
  • 7, slash, 4 kabi soddalashtirilgan notoʻgʻri kasr
  • 1, space, 3, slash, 4 kabi aralash son
  • 0, point, 75 kabi aniq oʻnli kasr
  • 12, space, start text, p, i, end text yoki 2, slash, 3, space, start text, p, i, end text kabi pi ning karralisi
d, equals
  • Javobingiz quyidagicha boʻlishi kerak:
  • 6 kabi butun son
  • 3, slash, 5 kabi soddalashtirilga toʻgʻri kasr
  • 7, slash, 4 kabi soddalashtirilgan notoʻgʻri kasr
  • 1, space, 3, slash, 4 kabi aralash son
  • 0, point, 75 kabi aniq oʻnli kasr
  • 12, space, start text, p, i, end text yoki 2, slash, 3, space, start text, p, i, end text kabi pi ning karralisi

Shunga oʻxshash masalalarni yechmoqchimisiz? Ushbu mashqni koʻring.

Oshkor formulani yozish

3, comma, 8, comma, 13, comma, point, point, point uchun oshkor formulani yozish kerak boʻlsin. Progressiya ayirmasi start color #ed5fa6, plus, 5, end color #ed5fa6 va birinchi had start color #11accd, 3, end color #11accd ga tengligi bizga maʼlum. Demak, progressiyaning oshkor formulasi quyidagicha boʻladi:
a, left parenthesis, n, right parenthesis, equals, start color #11accd, 3, end color #11accd, start color #ed5fa6, plus, 5, end color #ed5fa6, left parenthesis, n, minus, 1, right parenthesis
1-masala
  • Joriy
minus, 5, comma, minus, 1, comma, 3, comma, 7, comma, dots uchun oshkor formulani yozing.
a, left parenthesis, n, right parenthesis, equals

Shunga oʻxshash masalalarni yechmoqchimisiz? Ushbu mashqni koʻring.