Free Grade 3 Introducing Term-to-term Rules Quizzes
Free Grade 3 quizzes for Introducing 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing term-to-term rules
Identify introducing term-to-term rules accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing term-to-term rules
Explain introducing term-to-term rules accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing term-to-term rules
Calculate introducing term-to-term rules accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing term-to-term rules
Compare introducing 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 Introducing 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: 16, 18, 20, 22, …[1]
- 2.Find the next two terms: 13, 16, 19, 22, …[1]
- 3.Find the next two terms: 20, 23, 26, 29, …[1]
- 4.Find the next two terms: 20, 26, 32, 38, …[1]
- 5.Find the nth term of 12, 15, 18, 21, …[2]
- 6.Find the nth term of 6, 10, 14, 18, …[2]
- 7.Find the nth term of 12, 6, 0, -6, …[2]
- 8.Find the nth term of 4, 12, 20, 28, …[2]
- 9.Find the nth term of 10, 8, 6, 4, … and the 50th term.[3]
- 10.Find the nth term of 7, 2, -3, -8, … and the 50th term.[3]
- 11.Find the nth term of 12, 7, 2, -3, … and the 50th term.[3]
- 12.Find the nth term of 10, 6, 2, -2, … and the 50th term.[3]
Show answers and working
1. 24, 26
The difference is 2. 22 + 2 = 24, then 26.
2. 25, 28
The difference is 3. 22 + 3 = 25, then 28.
3. 32, 35
The difference is 3. 29 + 3 = 32, then 35.
4. 44, 50
The difference is 6. 38 + 6 = 44, then 50.
5. 3n + 9
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 12, so adjust by 9. nth term = 3n + 9
6. 4n + 2
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 6, so adjust by 2. nth term = 4n + 2
7. -6n + 18
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 12, so adjust by 18. nth term = -6n + 18
8. 8n − 4
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 4, so adjust by -4. nth term = 8n − 4
9. -2n + 12; 50th term = -88
Common difference -2, so start with -2n. -2 × 1 = -2; the first term is 10, so adjust by 12. nth term = -2n + 12
10. -5n + 12; 50th term = -238
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 7, so adjust by 12. nth term = -5n + 12
11. -5n + 17; 50th term = -233
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 12, so adjust by 17. nth term = -5n + 17
12. -4n + 14; 50th term = -186
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 10, so adjust by 14. nth term = -4n + 14
Worked examples
Find the next two terms: 20, 24, 28, 32, …
- The difference is 4.
- 32 + 4 = 36, then 40.
- Answer: 36, 40
Find the nth term of 5, 11, 17, 23, …
- Common difference 6, so start with 6n.
- 6 × 1 = 6; the first term is 5, so adjust by -1.
- nth term = 6n − 1
- Answer: 6n − 1
Find the nth term of 7, 1, -5, -11, … and the 50th term.
- Common difference -6, so start with -6n.
- -6 × 1 = -6; the first term is 7, so adjust by 13.
- nth term = -6n + 13
- Answer: -6n + 13; 50th term = -287
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
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Frequently asked
- Is this Grade 3 Introducing Term-to-term Rules quiz really free?
- Yes. Every quizzes 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 Inequalities. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Introducing Term-to-term Rules?
- Move on to Working with Term-to-term Rules, Term-to-term Rules in Context, nth Term of a Linear Sequence, Quadratic Sequences, which build directly on this idea.
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