Free Grade 3 Term-to-term Rules in Context Worksheets
Free Grade 3 worksheets for Term-to-term Rules in Context: 12 real questions with a full answer key and worked solutions. An arithmetic sequence goes up or down by the same amount each time. The nth term is (difference)n plus an adjustment.
Free
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain term-to-term rules in context
Explain term-to-term rules in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate term-to-term rules in context
Calculate term-to-term rules in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare term-to-term rules in context
Compare term-to-term rules in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify term-to-term rules in context
Justify term-to-term rules in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Term-to-term Rules in Context works
An arithmetic sequence goes up or down by the same amount each time. The nth term is (difference)n plus an adjustment.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Find the next two terms: 20, 27, 34, 41, …[1]
- 2.Find the next two terms: 6, 10, 14, 18, …[1]
- 3.Find the next two terms: 4, 12, 20, 28, …[1]
- 4.Find the next two terms: 15, 19, 23, 27, …[1]
- 5.Find the nth term of 10, 13, 16, 19, …[2]
- 6.Find the nth term of 9, 14, 19, 24, …[2]
- 7.Find the nth term of 6, 0, -6, -12, …[2]
- 8.Find the nth term of 6, 12, 18, 24, …[2]
- 9.Find the nth term of 14, 17, 20, 23, … and the 50th term.[3]
- 10.Find the nth term of 18, 26, 34, 42, … and the 50th term.[3]
- 11.Find the nth term of 5, -1, -7, -13, … and the 50th term.[3]
- 12.Find the nth term of 9, 7, 5, 3, … and the 50th term.[3]
Show answers and working
1. 48, 55
The difference is 7. 41 + 7 = 48, then 55.
2. 22, 26
The difference is 4. 18 + 4 = 22, then 26.
3. 36, 44
The difference is 8. 28 + 8 = 36, then 44.
4. 31, 35
The difference is 4. 27 + 4 = 31, then 35.
5. 3n + 7
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 10, so adjust by 7. nth term = 3n + 7
6. 5n + 4
Common difference 5, so start with 5n. 5 × 1 = 5; the first term is 9, so adjust by 4. nth term = 5n + 4
7. -6n + 12
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 6, so adjust by 12. nth term = -6n + 12
8. 6n + 0
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 6, so adjust by 0. nth term = 6n + 0
9. 3n + 11; 50th term = 161
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 14, so adjust by 11. nth term = 3n + 11
10. 8n + 10; 50th term = 410
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 18, so adjust by 10. nth term = 8n + 10
11. -6n + 11; 50th term = -289
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 5, so adjust by 11. nth term = -6n + 11
12. -2n + 11; 50th term = -89
Common difference -2, so start with -2n. -2 × 1 = -2; the first term is 9, so adjust by 11. nth term = -2n + 11
Worked examples
Find the next two terms: 5, 13, 21, 29, …
- The difference is 8.
- 29 + 8 = 37, then 45.
- Answer: 37, 45
Find the nth term of 17, 13, 9, 5, …
- Common difference -4, so start with -4n.
- -4 × 1 = -4; the first term is 17, so adjust by 21.
- nth term = -4n + 21
- Answer: -4n + 21
Find the nth term of 5, 0, -5, -10, … and the 50th term.
- Common difference -5, so start with -5n.
- -5 × 1 = -5; the first term is 5, so adjust by 10.
- nth term = -5n + 10
- Answer: -5n + 10; 50th term = -240
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Writes n + 3 for a sequence going up in 3s.
Correction: Going up in 3s means 3n.
Forgets to adjust for the first term.
Correction: Compare 3n with the actual sequence.
Teacher tips
- · Line the sequence up under the times table to find the adjustment.
Parent tips
- · Track weekly savings and predict week 10.
Real-life applications
- · Taxi fares, saving the same amount each week.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Term-to-term Rules in Context
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Term-to-term Rules in Context worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Term-to-term Rules, Introducing Term-to-term Rules, Inequalities. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Term-to-term Rules in Context?
- Move on to nth Term of a Linear Sequence, Quadratic Sequences, Geometric Sequences, which build directly on this idea.
Related resources
Stuck on Term-to-term Rules in Context? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor