Free Grade 3 Working with Term-to-term Rules Lessons
Free Grade 3 lessons for Working with Term-to-term Rules: 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
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with term-to-term rules
Identify working with term-to-term rules accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with term-to-term rules
Explain working with term-to-term rules accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with term-to-term rules
Calculate working with term-to-term rules accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with term-to-term rules
Compare working with term-to-term rules 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 Working with Term-to-term Rules 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: 4, 6, 8, 10, …[1]
- 2.Find the next two terms: 18, 20, 22, 24, …[1]
- 3.Find the next two terms: 7, 11, 15, 19, …[1]
- 4.Find the next two terms: 13, 17, 21, 25, …[1]
- 5.Find the nth term of 3, -1, -5, -9, …[2]
- 6.Find the nth term of 7, 15, 23, 31, …[2]
- 7.Find the nth term of 13, 19, 25, 31, …[2]
- 8.Find the nth term of 9, 12, 15, 18, …[2]
- 9.Find the nth term of 11, 10, 9, 8, … and the 50th term.[3]
- 10.Find the nth term of 13, 8, 3, -2, … and the 50th term.[3]
- 11.Find the nth term of 14, 22, 30, 38, … and the 50th term.[3]
- 12.Find the nth term of 1, -3, -7, -11, … and the 50th term.[3]
Show answers and working
1. 12, 14
The difference is 2. 10 + 2 = 12, then 14.
2. 26, 28
The difference is 2. 24 + 2 = 26, then 28.
3. 23, 27
The difference is 4. 19 + 4 = 23, then 27.
4. 29, 33
The difference is 4. 25 + 4 = 29, then 33.
5. -4n + 7
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 3, so adjust by 7. nth term = -4n + 7
6. 8n − 1
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 7, so adjust by -1. nth term = 8n − 1
7. 6n + 7
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 13, so adjust by 7. nth term = 6n + 7
8. 3n + 6
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 9, so adjust by 6. nth term = 3n + 6
9. -1n + 12; 50th term = -38
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 11, so adjust by 12. nth term = -1n + 12
10. -5n + 18; 50th term = -232
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 13, so adjust by 18. nth term = -5n + 18
11. 8n + 6; 50th term = 406
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 14, so adjust by 6. nth term = 8n + 6
12. -4n + 5; 50th term = -195
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 1, so adjust by 5. nth term = -4n + 5
Worked examples
Find the next two terms: 14, 17, 20, 23, …
- The difference is 3.
- 23 + 3 = 26, then 29.
- Answer: 26, 29
Find the nth term of 16, 10, 4, -2, …
- Common difference -6, so start with -6n.
- -6 × 1 = -6; the first term is 16, so adjust by 22.
- nth term = -6n + 22
- Answer: -6n + 22
Find the nth term of 4, 1, -2, -5, … and the 50th term.
- Common difference -3, so start with -3n.
- -3 × 1 = -3; the first term is 4, so adjust by 7.
- nth term = -3n + 7
- Answer: -3n + 7; 50th term = -143
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.
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Frequently asked
- Is this Grade 3 Working with Term-to-term Rules lesson really free?
- Yes. Every lessons 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 Introducing Term-to-term Rules, Inequalities. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Working with Term-to-term Rules?
- Move on to Term-to-term Rules in Context, nth Term of a Linear Sequence, Quadratic Sequences, Geometric Sequences, which build directly on this idea.
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