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Year 11
Higher

Sequence notation

I can define notation for sequences.

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New
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Year 11
Higher

Sequence notation

I can define notation for sequences.

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Lesson details

Key learning points

  1. Sequence notation becomes more formal in further studies.
  2. There is notation for a term, the next term and for general terms.
  3. You can use this notation to write the term-to-term rule.

Keywords

  • N^th term - The nth term of a sequence is the position of a term in a sequence where n stands for the term number.

  • Term-to-term - A term-to-term rule describes how to calculate the next term in the sequence from the previous term.

  • Fibonacci sequence - A Fibonacci sequence is a sequence where each term is the sum of the two previous terms.

Common misconception

Pupils may think that $$u_1$$ means that $$u$$ has a value of one.

$$u_1$$ refers to the first term in the sequence and $$u_2$$ refers to the second term. The subscript refers to the term number.

Pupils could generate their own term-to-term rules and have a peer try to generate three different sequences (three different starting values) and then compare the sequences. What is the same and what is different about these sequences?
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of these are the first 4 terms in the sequence with $$n^\text{th}$$ term rule $$4n+2$$?
2, 6, 10, 14, ...
4, 6, 8, 10, ...
6, 8, 10, 12, ...
Correct answer: 6, 10, 14, 18, ...
Q2.
What is the correct $$n^\text{th}$$ term rule for the linear sequence which starts 2, 7, 12, 17, ...?
$$2n + 7$$
$$2n + 5$$
Correct answer: $$5n -3$$
$$5n +2$$
Q3.
Match the first 4 terms of these sequences with possible term-to-term rules.
Correct Answer:3, 5, 7, 9, ...,Start on 3, add 2 to the previous term to get the next term.

Start on 3, add 2 to the previous term to get the next term.

Correct Answer:3, 5, 9, 17, ...,Start on 3, double then subtract 1 to get the next term.

Start on 3, double then subtract 1 to get the next term.

Correct Answer:3, 6, 9, 12, ...,Start on 3, add 3 to the previous term to get the next term.

Start on 3, add 3 to the previous term to get the next term.

Correct Answer:3, 6, 12, 24, ...,Start on 3, double the previous term to get the next term.

Start on 3, double the previous term to get the next term.

Correct Answer:3, 6, 15, 42, ...,Start on 3, subtract 1 then multiply by 3 to get the next term.

Start on 3, subtract 1 then multiply by 3 to get the next term.

Q4.
What term number is 51 in the linear sequence which starts: 3, 9, 15, 21, ...?
the $$8^\text{th}$$ term
Correct answer: the $$9^\text{th}$$ term
the $$15^\text{th}$$ term
the $$16^\text{th}$$ term
the $$17^\text{th}$$ term
Q5.
A Fibonacci sequence starts 7, 11, 18, ... what is the fourth term?
Correct Answer: 29
Q6.
A Fibonacci sequence has first term 4 and fourth term 14. What is the second term?
Correct Answer: 5

Exit quiz

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6 Questions

Q1.
Which of these would be the correct notation to refer to the third term in a sequence?
$$3n$$
$$3u$$
$$n_3$$
Correct answer: $$u_3$$
$$n^3$$
Q2.
Which of these could be correct notation for the linear sequence 5, 9, 13, 17, 21, ... ?
$$u_{n} = u_{n+1} + 4, u_1 = 5$$
Correct answer: $$u_{n+1} = u_{n} + 4, u_1 = 5$$
$$u_{n} = u_{n+4}, u_1 = 5$$
$$u_{n} = u(n+4), u_1 = 5$$
Q3.
Match these terms to their rules.
Correct Answer:4, 10, 22, 46, .. ,$$u_{n+1} = 2u_{n} + 2, u_1 = 4$$

$$u_{n+1} = 2u_{n} + 2, u_1 = 4$$

Correct Answer:1, 5, 13, 29, ... ,$$u_{n+1} = 2u_{n} + 3, u_1 = 1$$

$$u_{n+1} = 2u_{n} + 3, u_1 = 1$$

Correct Answer:1, 5, 17, 53, ... ,$$u_{n+1} = 3u_{n} + 2, u_1 = 1$$

$$u_{n+1} = 3u_{n} + 2, u_1 = 1$$

Correct Answer:4, 12, 28, 60, ... ,$$u_{n+1} = 2(u_{n} + 2), u_1 = 4$$

$$u_{n+1} = 2(u_{n} + 2), u_1 = 4$$

Q4.
A linear sequence has $$n^\text{th}$$ term rule $$5n +2$$ which of these could describe the same sequence?
$$u_{n+1} = u_{n} + 2 , u_1 = 5$$
$$u_{n+1} = u_{n} + 5 , u_1 = 2$$
Correct answer: $$u_{n+1} = u_{n} + 5 , u_1 = 7$$
$$u_{n+1} = 2u_{n} + 5 , u_1 = 2$$
$$u_{n+1} = 5u_{n} + 2 , u_1 = 7$$
Q5.
A sequence has rule $$u_{n+2} = u_{n} + u_{n+1} , u_1 = 6, u_2 = 2 $$. What is the $$5^\text{th}$$ term?
Correct Answer: 18
Q6.
A sequence has form $$u_{n+1}= ku_n -3 , u_1 = 2$$ If $$u_3 = 6$$ then $$k= -\frac{3}{2}$$ or $$k=$$
Correct Answer: 3