Free Grade 3 Working with Geometric Sequences Lessons
Free Grade 3 lessons for Working with Geometric 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
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with geometric sequences
Identify working with geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with geometric sequences
Explain working with geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with geometric sequences
Calculate working with geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with geometric sequences
Compare working with geometric 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 Working with Geometric 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: 15, 20, 25, 30, …[1]
- 2.Find the next two terms: 15, 18, 21, 24, …[1]
- 3.Find the next two terms: 6, 9, 12, 15, …[1]
- 4.Find the next two terms: 15, 23, 31, 39, …[1]
- 5.Find the nth term of 3, 2, 1, 0, …[2]
- 6.Find the nth term of 4, 7, 10, 13, …[2]
- 7.Find the nth term of 11, 18, 25, 32, …[2]
- 8.Find the nth term of 14, 9, 4, -1, …[2]
- 9.Find the nth term of 15, 21, 27, 33, … and the 50th term.[3]
- 10.Find the nth term of 9, 10, 11, 12, … and the 50th term.[3]
- 11.Find the nth term of 3, 4, 5, 6, … and the 50th term.[3]
- 12.Find the nth term of 13, 9, 5, 1, … and the 50th term.[3]
Show answers and working
1. 35, 40
The difference is 5. 30 + 5 = 35, then 40.
2. 27, 30
The difference is 3. 24 + 3 = 27, then 30.
3. 18, 21
The difference is 3. 15 + 3 = 18, then 21.
4. 47, 55
The difference is 8. 39 + 8 = 47, then 55.
5. -1n + 4
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 3, so adjust by 4. nth term = -1n + 4
6. 3n + 1
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 4, so adjust by 1. nth term = 3n + 1
7. 7n + 4
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 11, so adjust by 4. nth term = 7n + 4
8. -5n + 19
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 14, so adjust by 19. nth term = -5n + 19
9. 6n + 9; 50th term = 309
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 15, so adjust by 9. nth term = 6n + 9
10. 1n + 8; 50th term = 58
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 9, so adjust by 8. nth term = 1n + 8
11. 1n + 2; 50th term = 52
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 3, so adjust by 2. nth term = 1n + 2
12. -4n + 17; 50th term = -183
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 13, so adjust by 17. nth term = -4n + 17
Worked examples
Find the next two terms: 20, 28, 36, 44, …
- The difference is 8.
- 44 + 8 = 52, then 60.
- Answer: 52, 60
Find the nth term of 16, 11, 6, 1, …
- Common difference -5, so start with -5n.
- -5 × 1 = -5; the first term is 16, so adjust by 21.
- nth term = -5n + 21
- Answer: -5n + 21
Find the nth term of 2, 11, 20, 29, … and the 50th term.
- Common difference 9, so start with 9n.
- 9 × 1 = 9; the first term is 2, so adjust by -7.
- nth term = 9n − 7
- Answer: 9n − 7; 50th term = 443
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 Geometric 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 Introducing Geometric Sequences, Quadratic Sequences. 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 Geometric Sequences?
- Move on to Geometric Sequences in Context, Term-to-term Rules, nth Term of a Linear Sequence, Quadratic Sequences, which build directly on this idea.
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