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* Uzbek language added * Fibonaci series added into Uzbek * Update Fibonachi sonlari.md * Update uz/Boshlang'ich Matematika/Fibonachi sonlari.md Co-authored-by: David Leal <[email protected]> Co-authored-by: David Leal <[email protected]>
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# Arifmetik Progressiya | ||
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**Arifmetik progressiya** – ikkinchisidan boshlab har bir son oʻzidan oldingi songa shu qator uchun oʻzgarmas bir son **d** (progressiya ayirmasi)ni qoʻshishdan hosil boʻladigan sonlar qatori. | ||
Masalan, 2, 4, 6, 8, 10 sonlar qatori Arifmetik progressiyadir. Chunki, bu qatordagi har bir son oldingisidan bir xilga, 2ga farq qiladi. | ||
<p align="center"> | ||
<img width="60%" src="https://user-images.githubusercontent.com/75872316/122635132-ce38d100-d0ff-11eb-8fdf-2e14a9f640cc.png"> | ||
</p> | ||
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**Arifmetik Progressiyada:** | ||
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1. Arifmetik Progressiyaning birinchi elementi uning `birinchi hadi` deyiladi. | ||
2. hadlari orasidagi farqi esa Arifmetik Progressiyaning `ayirmasi` deyiladi. | ||
3. Arifmetik Progressiyaning o'suvchi yoki kamayuvchi bo'lishini uning `ayirmasi` ifodalayadi. Agar Arifmetik Progressiya `ayirmasi` musbat bo'lsa (`d>0`), `o'suvchi` agarda manfiy bo'lsa (`d<0`), kamayuvchi bo'ladi. | ||
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**Arifmetik Progressiyaning `n`chi hadini topish:** | ||
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a<sub>1</sub> - birinchi hadi va `d` esa arifmetik progressiya ayirmasi. Shulardan kelib chiqqan holatda umumiy formula quyidagicha bo'ladi: | ||
<p align="center"> | ||
<img width="60%" src="https://user-images.githubusercontent.com/75872316/122635193-25d73c80-d100-11eb-9015-344d36633704.png"> | ||
</p> | ||
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**Arifmetik Progressiyaning birinchi `n`ta hadini yig'indisini topish:** | ||
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<p align="center"> | ||
<img width="60%" src="https://user-images.githubusercontent.com/75872316/122635260-7a7ab780-d100-11eb-82a5-8ceeba3aff03.png"> | ||
</p> | ||
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**Arifmetik Progressiyaga oid masalalarni yechishni umumiy formulalari:** | ||
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Agar a<sub>1</sub> - birinchi xadi va uning ayirmasi - `d` bo'lsa: | ||
- **a<sub>n</sub>** = a<sub>1</sub> + (n-1)*d. | ||
- **Arifmetik o'rtanchasini topish:** S<sub>n</sub> / n. | ||
- **Dastlabki `n`tasini yig'indisi** `S = 0.5 n [ 2a + (n-1) d ]`. | ||
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# Manba | ||
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- [Arifmetik Progressiya](https://uz.khanacademy.org/math/algebra/sequences/introduction-to-arithmetic-squences/a/using-formulas-of-arithmetic-sequences) | ||
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# YouTube | ||
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- [Video materialga bog'ich](https://youtu.be/UVDpqDlBhyE) |
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# Fibonachi sonlari | ||
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Matematikada Fibonachi sonlari deb nomlanadigan sonlar qatori mavjud bo'lib, bu sonlar qatorida har bir son o'zidan | ||
avval kelgan ikkitda ketma-ket sonlarning yig'indisidan iboratdir. Fibonachi sonlar qatorining birinchi va ikkinchi | ||
hadlari mos ravishda 0 va 1ga tengdir. Quyidagi qator ham Fibonachi qatori hisoblanadi: | ||
`[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...]` | ||
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## Foydalanish | ||
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Biz Fibonachi sonlar qatorini asosan kompyterlarda qidirish algorithmi sifatida ko'rishimiz mumkin. Bundan tashqari bu | ||
qatorni bir hayotimizning quyidagi jabhalarida uchratib turishimiz mumkin: | ||
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- Daraxt barglarining o'zagida va daraxt shoxlarida uchratib turishimiz mumkin. | ||
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Hozirgi kunda Fibonachi sonlar qatori va Oltin nisbatga fizika, kvant mehanikasi va kriptografiya sohasida izlanish olib | ||
boruvchilar tomonidan katta qiziqishlar bildirilmoqda. | ||
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## Namuna | ||
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Fibonachi sonlarning 8chi hadini topishni ko'rib chiqamiz: | ||
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1-had | `f1 = 0` | ||
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2-had | `f2 = 1 ` | ||
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3-had | `f3 = f1+f2`=1 | ||
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4-had | `f4 = f2+f3`=2 | ||
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5-had | `f5 = f3+f4`=3 | ||
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6-had | `f6 = f4+f5`=5 | ||
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7-had | `f7 = f5+f6`=8 | ||
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8-had | `f8 = f6+f7`=13 | ||
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f(8)=21 | ||
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## Fibonachi algoritmning dasturlash tillaridagi ko'rinishi: | ||
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- [C++](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci.cpp) | ||
- [Java](https://github.com/TheAlgorithms/Java/blob/master/Maths/FibonacciNumber.java) | ||
- [Javascript](https://github.com/TheAlgorithms/Javascript/blob/80c2dc85d714f73783f133964d6acd9b5625ddd9/Maths/Fibonacci.js) | ||
- [Python](https://github.com/TheAlgorithms/Python/blob/master/maths/fibonacci.py) | ||
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## Video bog'ich | ||
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- [YouTube](https://youtu.be/FQiRf4jb3PU) | ||
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## Boshqa manbalar | ||
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- [Wikipedia](https://uz.wikipedia.org/wiki/Fibonachchi_sonlari) |
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