Arithmetic And Geometric Progressions
Bayani Gaba-gaba
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.
Manufura
- 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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Nazarin Darasi
Barka da kammala darasi akan Arithmetic And Geometric Progressions. Yanzu da kuka bincika mahimman ra'ayoyi da ra'ayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- 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
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
Littattafan da ake ba da shawarar karantawa
Ƙarin koyo daga tushe na buɗe
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Sashen littafi
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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Sashen littafi
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
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