Arithmetic And Geometric Progressions
Gbogbo ọrọ náà
Some sequences grow by adding the same amount each time; others grow by multiplying by the same factor. The first are arithmetic progressions, the second are geometric progressions, and together they describe an enormous range of patterns, from stacking chairs to compound interest to a bouncing ball.
In this lesson you will learn the formulas for the nth term and the sum of both kinds of progression, and the elegant sum to infinity of a geometric series when the common ratio is small enough. These compact formulas let you jump straight to the 100th term or the total of hundreds of terms without listing them all.
Ebumnobi
- Recognise arithmetic and geometric progressions and understand the difference between them.
- Use the formulas for the nth term and the sum of the first n terms, and the sum to infinity of a convergent geometric progression.
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Maapụ uche
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Akwụkwọ Ọmụmụ
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Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Arithmetic And Geometric Progressions. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- For the AP 3, 7, 11, 15, ..., what is the 10th term? A. 35 B. 39 C. 40 D. 43 Answer: B
- For the AP 3, 7, 11, 15, ..., what is the sum of the first 10 terms? A. 195 B. 200 C. 210 D. 220 Answer: C
- For the GP 2, 6, 18, 54, ..., what is the 5th term? A. 108 B. 144 C. 162 D. 216 Answer: C
- For the GP 2, 6, 18, ..., what is the sum of the first 5 terms? A. 162 B. 200 C. 242 D. 486 Answer: C
- What is the sum to infinity of 8, 4, 2, 1, ...? A. 8 B. 12 C. 16 D. infinite Answer: C
Rue ajuju ndi a n'ime ngwa ahu
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Akwụkwọ A Na-atụ Aro
Mụtakwuo ihe site na isi mmalite mepere emepe
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Akụkụ akwụkwọ
Series and Their Notations
Use summation notation.
"Algebra and Trigonometry: Series and Their Notations" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/13-4-series-and-their-notations. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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Akụkụ akwụkwọ
Arithmetic Sequences
Find the common difference for an arithmetic sequence.
"Algebra and Trigonometry: Arithmetic Sequences" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/13-2-arithmetic-sequences. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
Ndị otu ndị ọzọ bipụtara ha n'okpuru ikike mepere emepe, anyị na-ekele ha dị ka ha si chọọ. Njikọ na-emepe saịtị ha.
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Arithmetic And Geometric Progressions? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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