Number Sequences & Patterns Worksheets

Create Printable Number Sequence and Pattern Worksheets

Generate free printable number sequence worksheets covering the three classic pattern types: arithmetic (add or subtract a constant), geometric (multiply or divide by a constant), and quadratic (second differences constant).

Create worksheets in A4 or US Letter PDF format from Year 4 right through to Key Stage 3. Learners find the next term and state the rule, with an optional answer key for quick marking.

This number sequences generator helps parents, teachers, homeschoolers, and tutors give learners fresh pattern-spotting practice at exactly the right level for their year group.

Why use this number sequences generator?

Pattern recognition is a foundational mathematical habit — it's the bridge from arithmetic into algebra. Single-pattern and mixed sheets give learners the right kind of practice at each stage. Use it for:

• early sequence work in Year 4 and Year 5
• introducing "nth term" thinking in Year 6 and Year 7
• building up to quadratic sequences in Year 8 and Year 9
• mixed revision before algebra or SATs-style assessments
• tutor practice on specific pattern types

Because problems are regenerated on every export, pupils never run out of new sequences to spot.

What you can customise

The generator gives direct control over the type and size of the sequence:

• Pattern type: Arithmetic, Geometric, Quadratic, or Mixed
• Number of terms shown: Between 3 and 7 terms on the sheet
• Max step / multiplier: Caps the arithmetic common difference or geometric ratio
• Question count: How many problems fit on the page
• Include answer key: Appends a full answers page with next term and rule
• Worksheet title, name and date fields
• Paper size: A4 or US Letter PDF

Arithmetic sequences can include subtract-by rules, and geometric sequences can include halving, so learners meet both directions of change.

Notes and limitations

• Quadratic sequences are kept simple — typically of the form n² or n² + constant, so the rule is accessible.
• Geometric sequences with larger multipliers grow fast; keep the Max multiplier low if you want short terms.
• Asking for 7 terms with a large multiplier will produce big numbers — good for stretch, less good for Year 4.
• The "state the rule" answer is given in words ("add 4 each time", "multiply by 3 each time", "square the position").

Who these worksheets are for

Number sequences appear across almost the whole primary curriculum and well into secondary, so the generator is useful at many levels.

Parents

Support home practice on "find the next term" for Year 4 to Year 6, or harder quadratic practice for Year 8 revision.

Teachers

Use single-type sheets to introduce each pattern, then mixed sheets for consolidation and assessment.

Homeschool families

Follow a three-stage progression: arithmetic first, then geometric once multiplication tables are fluent, then quadratic as algebra begins.

Tutors

Target the pattern type the learner is least confident with — often quadratic — with a focused single-topic sheet.

Worksheet style options

Arithmetic sequences

Sequences where the same amount is added (or subtracted) each step: 3, 7, 11, 15… or 50, 42, 34, 26… The rule is a constant change. Best for Year 4 to Year 6.

Geometric sequences

Sequences where the same amount is multiplied (or divided) each step: 2, 6, 18, 54… or 64, 32, 16, 8… The rule is a constant multiplier. Best for Year 6 to Year 8 once multiplication is secure.

Quadratic sequences

Sequences whose second differences are constant: 1, 4, 9, 16, 25… or 2, 5, 10, 17, 26… The rule is a function of n². Best for Year 8 and Year 9 once algebraic notation is familiar.

Mixed

Mixed mode rotates all three, which is closer to exam revision where the learner has to decide the pattern type first.

How to use the tool

1. Choose the pattern type: arithmetic, geometric, quadratic, or mixed.
2. Set the number of terms shown on each problem.
3. Set the Max step or multiplier.
4. Pick the number of questions per sheet.
5. Turn Include answer key on or off.
6. Choose A4 or US Letter paper.
7. Click Generate to preview the worksheet.
8. Download the PDF.

Worked example

Pick Pattern type = Mixed with 5 terms shown. You might see "3, 7, 11, 15, 19, ___ (rule?)" where the next term is 23 and the rule is add 4 each time. A geometric question might read "2, 6, 18, 54, 162, ___" where the next term is 486 and the rule is multiply by 3 each time. A quadratic question might read "1, 4, 9, 16, 25, ___" where the next term is 36 and the rule is square the position number.

Methodology

The engine picks the pattern type, generates a rule (common difference, common ratio, or quadratic form), and builds the sequence term-by-term from a random starting value. The next term is computed from the same rule, so the printed next term and rule-in-words on the answer key always match.

Helpful preset ideas

• Arithmetic only, Max step 5, 5 terms, for Year 4
• Arithmetic only, Max step 10, 6 terms, for Year 5 to Year 6
• Geometric only, Max multiplier 3, 5 terms, for Year 7
• Quadratic only, 5 terms, for Year 8 to Year 9
• Mixed, 6 terms, for end-of-unit revision

Best ways to practise number sequences

• Always calculate the differences between consecutive terms first.
• If the first differences are not constant, check the second differences — that spots a quadratic.
• If the differences double or triple, the sequence is geometric, not arithmetic.
• Say the rule in words before writing the next term — this locks the pattern in.

Designed for A4 and US Letter Printing

Number sequence worksheets are produced as A4 or US Letter PDFs, so teachers in the UK and US can print cleanly without rescaling.

Related maths practice tools

You may also find these related tools useful:

• Introduction to Algebra Worksheets
• Equation Solving Worksheets
• Math Word Problems Generator
• Multiplication Table Generator