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Algebra I
Course: Algebra I > Unit 8
Lesson 4: Geometrik progressiyalarni qurish- Geometrik progressiyalar uchun aniq va rekurrent formulalar
- Geometrik progressiyalar uchun rekurrent formulalar
- Geometrik progressiyalar uchun aniq formulalar
- Geometrik progressiyaning rekurrent va aniq formulalarini bir-biriga oʻtkazish
- Geometrik progressiyaning rekurrent va aniq formulalarini bir-biriga oʻtkazish
- Geometrik progressiyalar tahlili
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Geometrik progressiyalar tahlili
Geometrik progressiyalarni tahlil qiling va ular bilan bogʻliq masalalarni yeching.
Geometrik progressiyaning qismlari va formulalari
Geometrik progressiyada ketma-ket hadlarning boʻlinmasi doim bir xil. Biz uni progressiya maxraji deb ataymiz.
Masalan, quyidagi progressiya maxraji 2 ga teng:
start color #ed5fa6, times, 2, \curvearrowright, end color #ed5fa6 | start color #ed5fa6, times, 2, \curvearrowright, end color #ed5fa6 | start color #ed5fa6, times, 2, \curvearrowright, end color #ed5fa6 | ||||
---|---|---|---|---|---|---|
1, comma | 2, comma | 4, comma | 8, comma, point, point, point |
Geometrik progressiya formulalari yordamida a, left parenthesis, n, right parenthesis, progressiyaning n, start text, negative, end texthadini topishimiz mumkin.
Quyida geometrik progressiyaning oshkor formulasi berilgan boʻlib, unda birinchi had start color #11accd, k, end color #11accd va progressiya maxraji start color #ed5fa6, r, end color #ed5fa6 ga teng.
Bu yuqoridagi progressiyaning rekursiv formulasi:
Geometrik progressiya haqida koʻproq maʼlumotga ega boʻlmoqchimisiz? Unda ushbu videoni koʻring.
Geometrik progressiyani kengaytirish
54, comma, 18, comma, 6, comma, point, point, point progressiyani kengaytirishimiz kerak boʻlsin. Koʻrinib turibdiki, har bir had oldingisidan start color #ed5fa6, times, start fraction, 1, divided by, 3, end fraction, end color #ed5fa6 ga farq qiladi:
start color #ed5fa6, times, start fraction, 1, divided by, 3, end fraction, \curvearrowright, end color #ed5fa6 | start color #ed5fa6, times, start fraction, 1, divided by, 3, end fraction, \curvearrowright, end color #ed5fa6 | |||
---|---|---|---|---|
54, comma | 18, comma | 6, comma, point, point, point |
Keyingi hadni topish uchun koʻpaytirishimiz kerak boʻlgan farq 2 ga teng:
start color #ed5fa6, times, start fraction, 1, divided by, 3, end fraction, \curvearrowright, end color #ed5fa6 | start color #ed5fa6, times, start fraction, 1, divided by, 3, end fraction, \curvearrowright, end color #ed5fa6 | start color #ed5fa6, times, start fraction, 1, divided by, 3, end fraction, \curvearrowright, end color #ed5fa6 | ||||
---|---|---|---|---|---|---|
54, comma | 18, comma | 6, comma | 2, comma, point, point, point |
Shunga oʻxshash masalalarni yechmoqchimisiz? Ushbu mashqni koʻring.
Rekursiv formulani yozish
54, comma, 18, comma, 6, comma, point, point, pointning rekursiv formulasini yozishimiz kerak boʻlsin. Biz bilamizki, progressiya maxraji start color #ed5fa6, start fraction, 1, divided by, 3, end fraction, end color #ed5fa6 ga teng. Bundan tashqari, birinchi had start color #11accd, 54, end color #11accd ga teng. Demak, quyidagi progressiya uchun rekursiv formula:
Shunga oʻxshash masalalarni yechmoqchimisiz? Ushbu misolni koʻring.
Oshkor formulani yozish
54, comma, 18, comma, 6, comma, point, point, point uchun oshkor formulani yozish kerak boʻlsin. Progressiya maxraji start color #ed5fa6, start fraction, 1, divided by, 3, end fraction, end color #ed5fa6 ga va birinchi had start color #11accd, 54, end color #11accd ga tengligi bizga maʼlum. Demak, progressiyaning oshkor formulasi quyidagicha boʻladi:
Shunga oʻxshash masalalarni yechmoqchimisiz? Ushbu misolni koʻring.
Muhokamaga qoʻshilmoqchimisiz?
Hozircha izohlar yoʻq.