icon-background-square
New
New
Year 8

Justifying terms of a sequence

I can determine whether a number is a term of a given arithmetic sequence.

icon-background-square
New
New
Year 8

Justifying terms of a sequence

I can determine whether a number is a term of a given arithmetic sequence.

warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

Lesson details

Key learning points

  1. A graph can be used to identify if a particular number is a term in a sequence.
  2. The nth term rule can be used to determine if a number is in the sequence .
  3. It is important to justify if a number is or is not a term in a sequence.

Keywords

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

Common misconception

It is impossible to tell if 174 368 is in the sequence -8,-3,2,7, ...

Generalising the rule for forming a given sequence can help us see if a value is in the sequence.


To help you plan your year 8 maths lesson on: Justifying terms of a sequence, download all teaching resources for free and adapt to suit your pupils' needs...

Graphical software can be used effective here to explore whether a given value is a term in a sequence.
speech-bubble
Teacher tip
copyright

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

Loading...

6 Questions

Q1.
The calculation 6(20) - 8 would find the 20$$^\text{th}$$ of the sequence $$6n-8$$.
Correct Answer: term
Q2.
Which of these describe features of the sequence $$5n-9$$?
Correct answer: It has a constant difference of +5
It decreases by 9 each time
The terms always end in the digits 1 or 6
Correct answer: The positive terms always end in the digits 1 or 6
Correct answer: It starts at -4
Q3.
What is the 75$$^\text{th}$$ term of the sequence $$6n-17$$?
675 - 17 = 658
6 + (75) - 17=64
Correct answer: 6(75) - 17 = 450 - 17 = 433
(6 - 17)75 = -11 $$\times$$ 75 = -825
Q4.
What happens when you plot an arithmetic sequence?
An image in a quiz
Correct answer: You get a straight line of values.
You get a decreasing pattern of values.
You get a curve.
Correct answer: You might see points in two quadrants.
You might plot points in all four quadrants.
Q5.
Calculate the 200$$^\text{th}$$ term of $$17.96-0.32n$$. You may use a calculator.
81.96
3528
-81.96
Correct answer: -46.04
Q6.
Put these term values in order of size. Start with the smallest.
1 - The 80$$^\text{th}$$ term of the sequence $$6n-35$$
2 - The 50$$^\text{th}$$ term of the sequence $$596-3n$$
3 - The 60$$^\text{th}$$ term of the sequence $$9n-88$$
4 - The 95$$^\text{th}$$ term of the sequence $$5n-11$$
5 - The 50$$^\text{th}$$ term of the sequence $$9n+19$$

6 Questions

Q1.
The sequence 37, 47, 57, 67, 77, ... could be described as which?
Correct answer: Linear
Non-linear
Correct answer: Arithmetic
Correct answer: Increasing
Decreasing
Q2.
Which of the below statements supports the justification that 6941 is not in the arithmetic sequence starting 14, 19, 24, 29, 34, ...?
It's too large a number.
Correct answer: 14, 19, 24, 29, 34, ... is a translation of a $$5n$$ sequence.
Correct answer: The sequence will always end in the digit 4 or 9 in the ones position.
6941 is an odd number, and the sequence begins with an even number.
Q3.
Which of the below will be common terms in the sequences $$2n+24$$ and $$5n+13$$?
Correct answer: 13 048
103
Correct answer: 888
1001
Correct answer: 8008
Q4.
The first 8 terms of a sequence are plotted. Which term is incorrect in the plotting of this arithmetic sequence?
An image in a quiz
The 2$$^\text{nd}$$ term
The 4$$^\text{th}$$ term
Correct answer: The 6$$^\text{th}$$ term
The 8$$^\text{th}$$ term
Q5.
Which of the below is a useful estimation to start with when trying to find 315 in the sequence $$6n-9$$?
$$n=25$$
Correct answer: $$n=50$$
$$n=100$$
$$n=300$$
$$n=600$$
Q6.
What does this calculator display tell us?
An image in a quiz
881 is in the sequence $$8n-17$$
Correct answer: 881 is not in the sequence $$8n-17$$
881 is the 112.25$$^\text{th}$$ term.
Correct answer: 881 is not a term because 112.25 is not a whole number.