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Geometrik progressiya bilan o‘yin

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Geometrik progressiya bilan o‘yin

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Geometriya: progressiya bo‘yicha qisqa o‘yin

Created by

Diyora Xayrullayeva
Diyora Xayrullayeva
Uzbekistan

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Geometrik progressiya bilan o‘yin
 

Geometrik progressiya bilan o‘yinOnline version

Geometriya: progressiya bo‘yicha qisqa o‘yin

by Diyora Xayrullayeva
1

1. Nima bu geometrik progressiya?

Geometrik progressiya — har bir ketma-ket term

avvalgi term bilan ma’lum bir nisbatda kamayib yoki ko‘payib boradigan ketma-ketlikdir.

2

2. Asosiy belgilar

Birinchi a1 - metrdagi boshlang‘ich qiymat; ikkinchi — r nisbat; an = a1 · r^(n-1) — n‑chi termin.

3

3. N-chi termin formulasi

a_n a1 va r yordamida oson hisoblanadi: a_n = a1 · r^(n-1).

4

4. Jamlanish formulasi (r ≠ 1)

Sum S_n = a1 · (1 − r^n) / (1 − r) — n ta term uchun umumiy yig‘indi.

5

5. R nisbatining yo‘qolishi

agar |r| < 1, n ta yakuniy yig‘indi converge (cheladi) bo‘ladi.

6

6. R ning bo‘lishi misollar

Misol: agar a1 = 3 va r = 2 bo‘lsa, a2 = 6, a3 = 12, va hk.

7

7. Yuqori kontekstlar

r > 0 bo‘lsa, ketma-ketlik muntazam ko‘payadi yoki kamayadi; r < 0 bo‘lsa, hakikatda sign o‘zgaradi.

8

8. Yig‘indi misoli

Masalan, a1 = 5, r = 1/2 bo‘lsa, S4 = 5 · (1 − (1/2)^4) / (1 − 1/2) = 9.5.

9

9. Amaliy qo‘llashlar

Moliyaviy banklar, sarmoya, va tez-tez kuzatiladigan o‘sish jarayonlarida geometrik progressiya keng qo‘llanadi.

10

10. Amaliy topshiriq

Topshiriq: a1 = 4, r = 3, hisoblang a5 va S5.
 
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