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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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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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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.


To help you plan your year 11 maths lesson on: Sequence notation, download all teaching resources for free and adapt to suit your pupils' needs...

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?
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This content is © Oak National Academy Limited (2025), 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.
tick

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.
tick

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.
tick

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.
tick

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.
tick

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

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

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

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

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

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

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

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

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