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Year 11
Higher

Conditions in arithmetic sequences

I can find the first value bigger or smaller than a given value in a sequence.

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New
New
Year 11
Higher

Conditions in arithmetic sequences

I can find the first value bigger or smaller than a given value in a sequence.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The n^th term rule can calculate the position of the value that is equal to the given value.
  2. If this is not an integer, then you can round down or up as needed.
  3. This term number can be used to generate the desired value.

Common misconception

Pupils may round the wrong way when finding the term number for a particular term value.

By calculating the terms either side of the non-integer value of $$n$$, pupils can easily determine what the rounded value of $$n$$ should be.

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.

Pupils can move from calculating the terms either side of the $$n$$ value by considering whether the sequence is increasing or decreasing and comparing this to whether they are looking for a value greater than or less than. This reasoning approach will be more appealing to some pupils.
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).

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Starter quiz

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6 Questions

Q1.
$$6n-7$$ is the __________ of the arithmetic sequence starting $$-1, 5, 11, 17, 23, ...$$
Correct answer: position-to-term rule
term-to-term rule
Correct answer: $$n^\text{th}$$ term rule
term value
Q2.
What is the $$n^\text{th}$$ term rule of the sequence $$14,22,30,38,46, ...$$?
$$n+14$$
$$n+8$$
$$14+8n$$
$$14n+8$$
Correct answer: $$8n+6$$
Q3.
What is the $$n^\text{th}$$ term rule of the sequence $$197,191,185,179,173, ...$$?
$$n-6$$
$$197n-6$$
$$197-6n$$
Correct answer: $$203-6n$$
$$203n-6$$
Q4.
What is the $$40^\text{th}$$ term of the sequence $$9n+51$$?
Correct Answer: 411, n=411
Q5.
What position is $$213$$ in the following arithmetic sequence? $$18,23,28,33, ...$$
Correct Answer: 40, 40th, n=40
Q6.
Solve the equation $$8n-37=495$$ If necessary leave your answer as a decimal. $$n=$$
Correct Answer: 66.5, n=66.5

Exit quiz

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6 Questions

Q1.
$$5n-28=100$$ is __________ we can solve in order to help us find the first term over $$100$$
an expression
a solution
Correct answer: an equation
a term-to-term rule
Q2.
Using trial and error, which is the best estimate at which to start to find the first value over $$1000$$ in the sequence starting $$-17,-13,-9,-5,-1, ...$$?
$$n=10$$
$$n=100$$
$$n=1000$$
$$n=25$$
Correct answer: $$n=250$$
Q3.
If you open a savings account with $$£50$$ and put $$£8$$ a week in to the account every week thereafter without withdrawing anything, after how many weeks will you reach $$£200$$?
4 weeks
Correct answer: 19 weeks
20 weeks
25 weeks
Q4.
Which term is the first value below $$−300$$ in the arithmetic sequence starting $$91, 83, 75, 67, 59, …$$?
The $$47^\text{th}$$ term
The $$48^\text{th}$$ term
The $$49^\text{th}$$ term
Correct answer: The $$50^\text{th}$$ term
The $$51^\text{st}$$ term
Q5.
The solution to $$2n-19=98$$ is $$n=58.5$$ What does this tell us about this sequence? $$-17,-15,-13,-11, ...$$
The $$58.5^\text{th}$$ term is $$98$$
The $$58^\text{th}$$ term is above $$98$$
Correct answer: The $$59^\text{th}$$ term is above $$98$$
Q6.
What is the last positive value in the sequence $$380, 365, 350, 335, ...$$?
$$n=26$$
Correct answer: $$5$$
$$n=27$$
$$10$$