Finding the nth Term: Free Printable Worksheet for Year 8
Finding the nth Term is a free printable worksheet for Year 8 (ages 12 to 13), in Key Stage 3. Find the rule for each number pattern. It comes from the Mini Minds Hub, a growing library of free printables from Jaques of London, the British games and toy company that has been making games for families since 1795.
It is two A4 pages. Page 1 is the activity for children. Page 2 is for the grown-up: it has notes on how to use the sheet, help for children who find it hard, a stretch idea, and the answers. Print it at home or in the classroom. Black and white printing works well.
What is on the sheet
This worksheet includes numbered questions with space to answer.
A look at what children will meet:
- 3, 5, 7, 9, ...
- 4, 7, 10, 13, ...
- 5, 10, 15, 20, ...
- 2, 6, 10, 14, ...
- 7, 9, 11, 13, ...
- 1, 5, 9, 13, ...
- 10, 20, 30, 40, ...
- 6, 11, 16, 21, ...
Who this is for
Year 8 (ages 12 to 13) in Key Stage 3.
Key Stage 3 covers Years 7 to 9, ages 11 to 14. Learners are moving from remembering facts to applying them, so tasks that ask for a reason or a method are worth more than quick answers. Use it at home, in class, on a rainy afternoon or at a family gathering.
What children practise
- Sequences
- Algebra
- nth term
Students find the nth term of a linear sequence.
Learning focus and curriculum link
Subject: Maths. Key stage: Key Stage 3. It supports the subject at this level through short, focused practice.
This sheet is a practice and play activity. It supports classroom learning and is not a replacement for it.
How to use it
- Print both pages. Page 1 is for the child. Keep page 2 for the grown-up.
- Work out the common difference first, then check the rule using term 1 and term 2.
- Work through the activity together the first time. Talk about each choice.
- Check against the notes on page 2 and the answers.
- Come back to it another day. Repeating a familiar activity builds confidence.
If it feels too hard
Write the multiples of the difference under the sequence.
To stretch confident children
Use the rule to find the 50th term of each sequence.
Make it a game
Make up your own sequence for a partner to solve.
Tips for parents and teachers
- Print on plain A4 paper. Black and white printing works too.
- Work through it together the first time, then let children try alone.
- Praise effort and thinking, not only correct answers.
A screen-free maths activity for Year 8
Children spend a lot of time on screens. This is a screen-free maths activity that needs only paper and a pencil. It works as quiet time after school, a rainy day activity, a holiday boredom buster or a calm moment before bed. Screen-free learning gives eyes a rest and gets children talking, thinking and writing by hand.
Free maths resources for teachers
Teachers can use this worksheet as a starter, a plenary, an early finisher task, a supply teacher resource, a homework task or a table activity. It needs no preparation beyond printing. The learning focus and skills are listed above so you can match it to your planning, and page 2 gives support and stretch ideas for mixed ability groups.
Maths ideas for parents at home
You do not need to be a teacher to use this. Read the sheet through, sit with your child for the first go and let them lead. Short bursts of ten to fifteen minutes work better than long sessions. If you are looking for free maths worksheets for Year 8, or simple home learning for the weekend or school holidays, this is a good place to start.
Home education and tutoring
Home educators and tutors can print this as part of a wider maths plan. It pairs well with books, outdoor play and everyday talk. Because the sheet is free and printable, you can use it again for brothers and sisters or for revision a few weeks later.
Why it helps children learn
Hands-on, paper based activities slow learning down in a good way. Children read carefully, think before they answer and see their own progress on the page. Games and challenges add a reason to keep going. That mix of play and practice is why printable activities like this are popular with parents, teachers and home educators.
Curriculum links for teachers
This sheet supports the areas below. It is matched to the published England frameworks. Please check it against your own school plan.
| Framework | Subject or area | Strand | Year |
|---|---|---|---|
| National Curriculum (England) | Maths | Algebra | Year 8 |
What children will be able to do
- I can find the common difference of a sequence.
- I can write the nth term of a linear sequence.
- I can use my rule to find any term.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- How did you find the rule for this sequence?
- What does the number in front of n tell you?
- How could you check your nth term is right?
More like this
- Area of a Circle
- Christmas Gift Budget Planner
- Expanding Brackets Dominoes
- Interior Angles of Polygons
Same subject, one year up: Mean Median Mode Poker | Same subject, one year down: Prime Number Pursuit
Frequently asked questions
What age is Finding the nth Term for?
It is written for Year 8 (ages 12 to 13), in Key Stage 3.
What will children practise?
Students find the nth term of a linear sequence.
How do I use it?
Work out the common difference first, then check the rule using term 1 and term 2.
What if it feels too hard?
Write the multiples of the difference under the sequence.
Is it free?
Yes. It is free to print for home and classroom use.
Is Finding the nth Term suitable for teachers to use in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing.
Is this a screen-free activity?
Yes. It is a screen-free printable that needs only paper and a pencil, so it works well for quiet time, rainy days and school holidays.
Can I use it for home education?
Yes. Home educators and tutors can use it on its own or as part of a wider plan. It is free to print again for brothers, sisters or revision.
How long does it take?
Most children finish page 1 in 10 to 20 minutes. The notes on page 2 suggest ways to make it shorter or longer.
Do I need to print in colour?
No. It prints well in black and white on plain A4 paper.
More free printables
More for Key Stage 3 | More maths printables | Free printable games | All Mini Minds Hub resources