Skip to content
Oak National Academy
Oak National Academy
Teachers
Pupils
New
New
Year 8

Finding the nth term

I can find the n^th term rule by investigating the common difference.

Download all resources
Share activities with pupils

Link copied to clipboard

New
New
Year 8

Finding the nth term

I can find the n^th term rule by investigating the common difference.

Download all resources
Share activities with pupils

Link copied to clipboard

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.

View new resources

Lesson details

Key learning points

  1. Finding the common difference can help when finding the n^th term rule.
  2. Comparing the sequence to an appropriate multiplication table can help identify the translation that has been made.
  3. The n^th term can be found for all arithmetic sequences.
  4. The n^th term rule can be used to identify the term number of a given number in a sequence.

Keywords

  • 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

That the sequence 6,11,16,21, ... is 5n+6 because it goes up by 5 and starts at 6.

Compare 6,11,16,21, ... to 5,10,15,20, ... "What is the shift? The translation? If that is 5n then this is 5n with how much more?"


To help you plan your year 8 maths lesson on: Finding the nth term, download all teaching resources for free and adapt to suit your pupils' needs...

Get students to explain back to you why 6,11,16,21, ... is 5n+1 and NOT 5n+6. If they can counter-argue the misconception then they truly understand what is going on here.
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

Skip lesson video

Loading...

Starter quiz

Download starter quiz

6 Questions

Q1.
The n$$^\text{th}$$ term is the position of a term in a sequence ($$n$$ is the term number). It can be used to calculate any term so is also known as a __________ for finding the n$$^\text{th}$$ term.
Correct answer: formula
sequence
variable
Q2.
What is the term-to-term rule for this pattern sequence?
An image in a quiz
Multiply by 3
Goes up by 1
Multiply by 3 and add 1
Correct answer: Add 3
Q3.
What is the position-to-term rule for this pattern sequence?
An image in a quiz
Multiply the term number by 3
Add 1 to the previous term
Correct answer: Multiply the term number by 3 and add 1
Add 3 to the previous term
Q4.
Which of these are arithmetic (linear) sequences?
1, 2, 4, 8, ...
1, 4, 8, 13, ...
Correct answer: 1, 4, 7, 10, ...
Correct answer: 10, 7, 4, 1, ...
Correct answer: 0.4, 0.7, 1, 1.3, ...
Q5.
This pattern represents people seated around an increasing number of tables. If you were asked to find the number of people around 50 tables, which calculation would you do?
An image in a quiz
$$50 \times 4$$
$$50 \times 2 + 4$$
$$50 \times 6$$
$$4 + 4 + 4 + 4 + 4 + \;$$... fifty times.
Correct answer: $$50 \times 4 + 2$$
Q6.
Order these arithmetic sequences in terms of the size of their common difference. Start with the greatest common difference.
1 - -101, -87, -73, -59, ...
2 - 124, 133, 142, 151, ...
3 - -8, 0, 8, 16, 24, ...
4 - -5, 2.5, 10, 17.5 ...
5 - 1852, 1859, 1866, 1873, ...
6 - 1896, 1888, 1880, 1872, ...
7 - 2190, 2180, 2170, 2160, ...

Exit quiz

Download exit quiz

6 Questions

Q1.
5$$n$$ - 2 is the __________ of the sequence 3, 8, 13, 18, ...
expression
Correct answer: $$n^\text{th}$$ term
unknown
term-to-term rule
Q2.
To find the $$n^\text{th}$$ term of an arithmetic sequence, which of the following do we need?
The 1$$^\text{st}$$ term
Correct answer: The common difference
The last term
Correct answer: The translation
The increase.
Q3.
17, 21, 25, 29, ... is a translation of what from the sequence 4$$n$$?
+17
+21
Correct answer: +13
It is not a translation of 4$$n$$.
+4
Q4.
What is the $$n^\text{th}$$ term of the arithmetic sequence 10, 15, 20, 25, ...?
$$5n+10$$
Correct answer: $$5n+5$$
$$10n+5$$
$$10n-5$$
+5
Q5.
The sequence $$17-7n$$ has a common difference of what?
17
-17
7
Correct answer: -7
Q6.
Find the $$n^\text{th}$$ term of the sequence 2.31, 2.22, 2.13, 2.04, ...
$$0.09n-2.31$$
$$2.31-0.09n$$
$$-0.09n$$
Correct answer: $$2.4-0.09n$$
$$2.04+0.09n$$