Sequences
Overview
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.
Objectives
- [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
Mind map
This topic is mapped out so you can see how the ideas connect.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Sequences. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- 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
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Work through these questions in the app
Recommended Books
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