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Year 11
Higher

Reasoning about values in an arithmetic sequence

I can reason whether a value appears in a given sequence.

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New
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Year 11
Higher

Reasoning about values in an arithmetic sequence

I can reason whether a value appears in a given sequence.

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Share activities with pupils
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Lesson details

Key learning points

  1. It is possible to generate the sequence and therefore show whether a value appears in the sequence.
  2. It is possible to use your knowledge of multiples to reason whether a value appears in a given 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 nth 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'. The tasks in this lesson help pupils explore two alternative methods to 'counting on'. Encourage them to reflect on the methods and consider when one is more appropriate than the others and when it does not matter.
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.
In sequences an $$n^\text{th}$$ term rule is a __________-to-term rule.
term
Correct answer: position
solution
Q2.
Match these sequences to their respective $$n^\text{th}$$ term rules.
Correct Answer:$$3,6,9,12,15, ...$$,$$3n$$

$$3n$$

Correct Answer:$$5,8,11,14,17, ...$$,$$3n+2$$

$$3n+2$$

Correct Answer:$$5,10,15,20,25, ...$$,$$5n$$

$$5n$$

Correct Answer:$$7,12,17,22,27, ...$$,$$5n+2$$

$$5n+2$$

Correct Answer:$$1,6,11,16,21, ...$$,$$5n-4$$

$$5n-4$$

Correct Answer:$$1,4,7,10,13, ...$$,$$3n-2$$

$$3n-2$$

Q3.
What is the $$15^\text{th}$$ term of the sequence $$4n-12$$?
Correct Answer: 48
Q4.
What is the $$15^\text{th}$$ term of the sequence $$12-4n$$?
Correct Answer: -48
Q5.
Solve the equation $$6n-35=331$$ $$n=$$
Correct Answer: 61, n=61
Q6.
Solve the equation $$35-6n=-487$$ $$n=$$
Correct Answer: 87, n=87

Exit quiz

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6 Questions

Q1.
If $$4832$$ is in the sequence $$5n-13$$ then $$5n-13=4832$$ must have a __________.
solution
positive solution
Correct answer: positive integer solution
positive non-integer solution
negative integer solution
Q2.
What is the $$n^\text{th}$$ term rule for the sequence $$-14,-11,-8,-5,-2,1, ...$$?
$$-17-3n$$
$$-14-3n$$
$$17-3n$$
$$3n-14$$
Correct answer: $$3n-17$$
Q3.
Is $$406$$ in the sequence $$-14,-11,-8,-5,-2,1, ...$$?
Correct answer: Yes - the $$n^\text{th}$$ term rule is $$3n-17$$
Yes - the $$n^\text{th}$$ term rule is $$-3n-14$$
No - the $$n^\text{th}$$ term rule is $$3n-17$$
No - the $$n^\text{th}$$ term rule is $$-3n-14$$
Q4.
How might you show that $$1138$$ is not in the sequence $$7n-19$$?
By explaining that $$1138$$ is even but all positive terms of $$7n-19$$ are odd.
By calculating the first few terms and 'counting on'.
Correct answer: By forming and solving an equation and showing that $$n$$ is not an integer.
By forming and solving an equation and showing that $$n$$ is a positive integer.
Q5.
What is true of the arithmetic sequence $$24, 29, 34, 39, 44, ...$$?
$$3428$$ will be a term.
Correct answer: $$3429$$ will be a term.
The terms will always be odd.
Correct answer: $$3824$$ will be a term.
$$-344$$ will be a term.
Q6.
$$707$$ is the $$53^\text{rd}$$ term and $$720$$ the $$54^\text{th}$$ term of an arithmetic sequence. Which of these terms are in the same sequence?
Correct answer: $$538$$
$$550$$
Correct answer: $$577$$
Correct answer: $$824$$
$$864$$