Sequences
Akopọ
Here are five numbers: 11, 15, 21, 29, 39. What is the hundredth? You could keep adding, and after ninety five more additions you would have it, provided you made no slips. Or you could find the rule that turns the position of a term into the term itself, put 100 into it, and be finished in one line. That gap, between grinding forward and jumping straight there, is what this topic is about.
You will generate terms of a sequence from either a term-to-term rule or a position-to-term rule, recognise and use sequences of triangular, square and cube numbers along with simple arithmetic progressions, and deduce expressions to calculate the nth term of linear sequences. On the Extension Tier the same two statements are extended to quadratic sequences, where the terms rise by a changing amount and the rule contains an \( n^2 \) term.
Awọn Afojusun
- [Core] generate terms of a sequence from either a term-to-term or a position-to-term rule
- [Core] recognise and use sequences of triangular, square and cube numbers and simple arithmetic progressions
- [Extension] including quadratic sequences
- [Core] deduce expressions to calculate the nth term of linear sequences
- [Extension] including quadratic sequences
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Ìdánwò Ẹ̀kọ́
Oriire fun ipari ẹkọ lori Sequences. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- What is the nth term of the sequence 7, 11, 15, 19, 23? A. n + 4 B. 4n C. 4n + 3 D. 4n + 7 Answer: C
- Which of these is the sequence of triangular numbers? A. 1, 4, 9, 16, 25 B. 1, 3, 6, 10, 15 C. 1, 8, 27, 64, 125 D. 2, 4, 8, 16, 32 Answer: B
- A sequence has constant second differences of 6. What is the coefficient of n^2 in its nth term? A. 2 B. 3 C. 6 D. 12 Answer: B
- A sequence has first term 5 and the term-to-term rule multiply by 2 and subtract 3. What is the third term? A. 7 B. 11 C. 14 D. 19 Answer: B
- Is 100 a term of the sequence with nth term 5n - 2? A. Yes, it is the 20th term B. Yes, it is the 21st term C. No, because 5n = 102 gives n = 20.4 D. No, because all terms are even Answer: C
Ṣiṣẹ́ lórí àwọn ìbéèrè wọ̀nyí nínú ohun èlò náà
Ṣiṣẹ́ lórí àwọn ìbéèrè wọ̀nyí nínú ohun èlò náà
Awọn Iwe Itọsọna Ti a Gba Nimọran
Ẹ̀kọ́ síwájú láti àwọn orísun ṣíṣí
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Abala ìwé ẹ̀kọ́
Sequences
Write the first few terms of a sequence
"Intermediate Algebra: Sequences" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/intermediate-algebra/pages/12-1-sequences. Access for free at https://openstax.org/books/intermediate-algebra/pages/1-introduction
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Abala ìwé ẹ̀kọ́
Arithmetic Sequences
Determine if a sequence is arithmetic
"Intermediate Algebra: 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/intermediate-algebra/pages/12-2-arithmetic-sequences. Access for free at https://openstax.org/books/intermediate-algebra/pages/1-introduction
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Ṣe Adaṣe Awọn Ibeere Idanwo Adaṣe
Ṣe o fẹ ṣe adaṣe awọn ibeere idanwo adaṣe nipa Sequences? Ṣe igbasilẹ ohun elo Green Bridge CBT lati wọle si awọn ibeere idanwo adaṣe ati awọn ayẹwo adaṣe kikun fun koko-ọrọ yii.
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