Free Grade 3 Sequences Lessons
Free Grade 3 lessons for Sequences: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain sequences
Explain sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate sequences
Calculate sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare sequences
Compare sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify sequences
Justify sequences 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 Sequences 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: 18, 23, 28, 33, …[1]
- 2.Find the next two terms: 19, 22, 25, 28, …[1]
- 3.Find the next two terms: 18, 21, 24, 27, …[1]
- 4.Find the next two terms: 17, 19, 21, 23, …[1]
- 5.Find the nth term of 20, 21, 22, 23, …[2]
- 6.Find the nth term of 8, 6, 4, 2, …[2]
- 7.Find the nth term of 15, 11, 7, 3, …[2]
- 8.Find the nth term of 8, 2, -4, -10, …[2]
- 9.Find the nth term of 9, 8, 7, 6, … and the 50th term.[3]
- 10.Find the nth term of 14, 19, 24, 29, … and the 50th term.[3]
- 11.Find the nth term of 12, 16, 20, 24, … and the 50th term.[3]
- 12.Find the nth term of 20, 14, 8, 2, … and the 50th term.[3]
Show answers and working
1. 38, 43
The difference is 5. 33 + 5 = 38, then 43.
2. 31, 34
The difference is 3. 28 + 3 = 31, then 34.
3. 30, 33
The difference is 3. 27 + 3 = 30, then 33.
4. 25, 27
The difference is 2. 23 + 2 = 25, then 27.
5. 1n + 19
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 20, so adjust by 19. nth term = 1n + 19
6. -2n + 10
Common difference -2, so start with -2n. -2 × 1 = -2; the first term is 8, so adjust by 10. nth term = -2n + 10
7. -4n + 19
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 15, so adjust by 19. nth term = -4n + 19
8. -6n + 14
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 8, so adjust by 14. nth term = -6n + 14
9. -1n + 10; 50th term = -40
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 9, so adjust by 10. nth term = -1n + 10
10. 5n + 9; 50th term = 259
Common difference 5, so start with 5n. 5 × 1 = 5; the first term is 14, so adjust by 9. nth term = 5n + 9
11. 4n + 8; 50th term = 208
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 12, so adjust by 8. nth term = 4n + 8
12. -6n + 26; 50th term = -274
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 20, so adjust by 26. nth term = -6n + 26
Worked examples
Find the next two terms: 2, 4, 6, 8, …
- The difference is 2.
- 8 + 2 = 10, then 12.
- Answer: 10, 12
Find the nth term of 5, 8, 11, 14, …
- Common difference 3, so start with 3n.
- 3 × 1 = 3; the first term is 5, so adjust by 2.
- nth term = 3n + 2
- Answer: 3n + 2
Find the nth term of 16, 19, 22, 25, … and the 50th term.
- Common difference 3, so start with 3n.
- 3 × 1 = 3; the first term is 16, so adjust by 13.
- nth term = 3n + 13
- Answer: 3n + 13; 50th term = 163
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 Sequences
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Frequently asked
- Is this Grade 3 Sequences 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 Inequalities, Equations, Number Sense. 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 Sequences?
- Move on to Quadratics, Simultaneous Equations, Functions, Number Sense, which build directly on this idea.
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