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Year 11
Higher

Identifying values in an arithmetic sequence

I can identify through the n^th term whether a value appears in a given sequence.

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New
New
Year 11
Higher

Identifying values in an arithmetic sequence

I can identify through the n^th term whether a value appears in a given sequence.

Download all resources
arrow-right
Share activities with pupils
arrow-right

Lesson details

Key learning points

  1. The n^th term rule can identify what term number a given number is.
  2. If the term number is not a positive integer, then the term is not in the sequence.

Keywords

  • Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

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

Common misconception

As long as the equation can be solved, the value will be in the sequence.

For the value to be in the sequence, the value for $$n$$ must be a positive integer. If it is not, then the value is not in the sequence as the term number must be a positive integer.

Pupils may not see why they need a different method to 'counting on'. Ask them to calculate the term value for a large term number such as 1987 to help them see why. The sequence could be made more tricky by having a negative common difference such as -17
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.
An arithmetic sequence has a common additive difference between successive terms. They are also frequently called __________ sequences.
Correct answer: linear
increasing
adding up
geometric
Q2.
In the linear equation $$y=6x-3$$ what is the value of $$y$$ when $$x=3$$?
Correct Answer: 15, y=15
Q3.
In the linear equation $$y=6x-3$$ what is the value of $$x$$ when $$y=3$$?
Correct Answer: 1, x=1
Q4.
Match the $$x$$ values to their respective $$y$$ values for the linear equation $$y=5-7x$$
Correct Answer:$$x=1$$,$$y=-2$$

$$y=-2$$

Correct Answer:$$x=2$$,$$y=-9$$

$$y=-9$$

Correct Answer:$$x=3$$,$$y=-16$$

$$y=-16$$

Correct Answer:$$x=4$$,$$y=-23$$

$$y=-23$$

Correct Answer:$$x=5$$,$$y=-30$$

$$y=-30$$

Correct Answer:$$x=10$$,$$y=-65$$

$$y=-65$$

Q5.
Solve the equation $$3x-17=451$$ $$x=$$
Correct Answer: 156, x=156
Q6.
Solve the equation $$4x+81=1000$$ and give your answer as a decimal. $$x=$$
Correct Answer: 229.75, x=229.75

Exit quiz

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6 Questions

Q1.
In sequence notation, $$T$$ is the term and $$n$$ is the term's __________.
Correct answer: position in the sequence
value
additive difference
Q2.
Which of these are the first three terms of the sequence $$2n-1$$?
Correct answer: $$1$$
$$2$$
Correct answer: $$3$$
$$4$$
Correct answer: $$5$$
Q3.
Which of these are the first five terms of the sequence $$20-7n$$?
$$20,13,6,-1,-8,...$$
$$20,13,6,-2,-9,...$$
Correct answer: $$13,6,-1,-8,-15...$$
$$13,6,-2,-9,-16...$$
Q4.
What is the $$50^\text{th}$$ term of the sequence $$8n-38$$?
Correct Answer: 362
Q5.
What position is the term 258 in the sequence $$8n-38$$?
Correct Answer: 37, 37th, n=37
Q6.
Which of the below are in the sequence $$12n-15$$?
Correct answer: $$285$$
$$290$$
Correct answer: $$993$$
Correct answer: $$1197$$
$$1200$$