New
New
Year 11
Foundation

Conditions in arithmetic sequences

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

New
New
Year 11
Foundation

Conditions in arithmetic sequences

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

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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.

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

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.


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

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 (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

Prior knowledge starter quiz

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6 Questions

Q1.
6n7 is the __________ of the arithmetic sequence starting 1,5,11,17,23,...
Correct answer: position-to-term rule
term-to-term rule
Correct answer: nth term rule
term value
Q2.
What is the nth 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 nth term rule of the sequence 197,191,185,179,173,...?
n6
197n6
1976n
Correct answer: 2036n
203n6
Q4.
What is the 40th 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 8n37=495 If necessary leave your answer as a decimal. n=
Correct Answer: 66.5, n=66.5

Assessment exit quiz

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6 Questions

Q1.
5n28=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 47th term
The 48th term
The 49th term
Correct answer: The 50th term
The 51st term
Q5.
The solution to 2n19=98 is n=58.5 What does this tell us about this sequence? 17,15,13,11,...
The 58.5th term is 98
The 58th term is above 98
Correct answer: The 59th 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
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