University of business and science

×2↷\footnotesize\maroonC{\times 2\,\Large\curvearrowright}×2↷start color #ed5fa6, times, 2, \curvearrowright, end color #ed5fa6		×2↷\footnotesize\maroonC{\times 2\,\Large\curvearrowright}×2↷start color #ed5fa6, times, 2, \curvearrowright, end color #ed5fa6
1,1,1,1, comma		2,2,2,2, comma		4,4,4,4, comma		8,...8,...8,...8, comma, point, point, point

Geometrik progressiya formulalari yordamida a(n)a(n)a(n)a, left parenthesis, n, right parenthesis, progressiyaning n-n{\text{-}}n-n, start text, negative, end texthadini topishimiz mumkin.
Quyida geometrik progressiyaning oshkor formulasi berilgan boʻlib, unda birinchi had k\blueD kkstart color #11accd, k, end color #11accd va progressiya maxraji r\maroonC rrstart color #ed5fa6, r, end color #ed5fa6 ga teng.
a(n)=k⋅rn−1a(n)=\blueD k\cdot\maroonC r^{n-1}a(n)=k⋅rn−1a, left parenthesis, n, right parenthesis, equals, start color #11accd, k, end color #11accd, dot, start color #ed5fa6, r, end color #ed5fa6, start superscript, n, minus, 1, end superscript
Bu yuqoridagi progressiyaning rekursiv formulasi:
{a(1)=ka(n)=a(n−1)⋅r\begin{cases}a(1) = \blueD k \\\\ a(n) = a(n-1)\cdot\maroonC r \end{cases}⎩⎪⎪⎨⎪⎪⎧​a(1)=ka(n)=a(n−1)⋅r​
Geometrik progressiya haqida koʻproq maʼlumotga ega boʻlmoqchimisiz? Unda ushbu videoni koʻring.


Geometrik progressiyani kengaytirish
54,18,6,...54,18,6,...54,18,6,...54, comma, 18, comma, 6, comma, point, point, point progressiyani kengaytirishimiz kerak boʻlsin. Koʻrinib turibdiki, har bir had oldingisidan ×13\maroonC{\times\dfrac{1}{3}}×31​start color #ed5fa6, times, start fraction, 1, divided by, 3, end fraction, end color #ed5fa6 ga farq qiladi: