MathsFreePrintable
Linear Pattern Equations
A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
Name:Date:
Linear Pattern Equations
Use n for the term position unless another variable is given. Show your working for calculation questions.
Recognising Linear Patterns
1.For the sequence 6, 10, 14, 18, …, state the constant difference and find the 9th term.
2.Which sequences have the same difference between every pair of consecutive terms? Select all that apply.
- 3, 6, 12, 24, …
- 8, 13, 18, 23, …
- 2, 5, 10, 17, …
- 12, 9, 6, 3, …
3.A sequence begins 7, 11, 15, 19, … . Complete the missing terms at positions 5 and 6.
Writing Equations for Patterns
4.A linear pattern starts 4, 9, 14, 19, … . Give its constant difference, its first term, and a rule for the term at position n.
5.Match each sequence to its rule. Use each rule once.
- Sequence A: 3, 5, 7, 9, …
- Sequence B: 4, 10, 16, 22, …
- Sequence C: 5, 9, 13, 17, …
- Sequence D: 7, 13, 19, 25, …
- y = 2n + 1
- y = 6n + 1
- y = 6n − 2
- y = 4n + 1
6.Find a rule for the sequence 12, 16, 20, 24, …, where n is the term position.
7.Which equation gives the sequence 9, 14, 19, 24, … when n = 1 is the first term position?
- y = 5n + 4
- y = 5n + 9
- y = 4n + 5
- y = 9n + 5
Predicting Terms and Solving Problems
8.A pattern follows y = 4n + 3. Find the 12th term, the 20th term, and the term position where y = 47.
9.A rainwater tank contains 420 litres after 1 minute, 570 litres after 2 minutes, and 720 litres after 3 minutes. Find the amount added each minute, the amount in the tank at minute 0, a rule for total litres L after m minutes, and the amount after 8 minutes.
10.A sequence has rule y = 7n − 2. What is its 6th term?
Check Your Understanding
11.A student says that a sequence is linear if the difference between consecutive terms stays constant. Is this statement true or false?
12.Does y = 3n describe the sequence 3, 6, 9, 12, … when n begins at 1?
13.If a sequence begins at 8 and increases by 4 each term, its rule is y = 4n + 4. Is this correct?
14.Explain how the common difference and the first term help you form a rule for a linear pattern.
3 printable pages
Page 1
Page 2
Page 3
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
More Maths Worksheets
Year 7–8
Algebra Language Basics
Free
Year 8
Algebraic Properties Application
Free
Year 7–8
Number and Algebra Basics
Free
Year 9
Algebra Scavenger Hunt
Free
Year 7–8
Introduction to Algebraic Concepts
Free
Year 7–8
Unknown Angles Equations
Free
Year 7–8
Patterns to Algebra
Free
Year 11