Free Grade 3 Geometric Sequences Worksheets
Free Grade 3 worksheets for 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify geometric sequences
Identify geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain geometric sequences
Explain geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate geometric sequences
Calculate geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare geometric sequences
Compare 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 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: 4, 7, 10, 13, …[1]
- 2.Find the next two terms: 7, 10, 13, 16, …[1]
- 3.Find the next two terms: 19, 23, 27, 31, …[1]
- 4.Find the next two terms: 5, 9, 13, 17, …[1]
- 5.Find the nth term of 10, 15, 20, 25, …[2]
- 6.Find the nth term of 9, 8, 7, 6, …[2]
- 7.Find the nth term of 5, 2, -1, -4, …[2]
- 8.Find the nth term of 15, 18, 21, 24, …[2]
- 9.Find the nth term of 9, 18, 27, 36, … and the 50th term.[3]
- 10.Find the nth term of 19, 27, 35, 43, … and the 50th term.[3]
- 11.Find the nth term of 5, 12, 19, 26, … and the 50th term.[3]
- 12.Find the nth term of 10, 7, 4, 1, … and the 50th term.[3]
Show answers and working
1. 16, 19
The difference is 3. 13 + 3 = 16, then 19.
2. 19, 22
The difference is 3. 16 + 3 = 19, then 22.
3. 35, 39
The difference is 4. 31 + 4 = 35, then 39.
4. 21, 25
The difference is 4. 17 + 4 = 21, then 25.
5. 5n + 5
Common difference 5, so start with 5n. 5 × 1 = 5; the first term is 10, so adjust by 5. nth term = 5n + 5
6. -1n + 10
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 9, so adjust by 10. nth term = -1n + 10
7. -3n + 8
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 5, so adjust by 8. nth term = -3n + 8
8. 3n + 12
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 15, so adjust by 12. nth term = 3n + 12
9. 9n + 0; 50th term = 450
Common difference 9, so start with 9n. 9 × 1 = 9; the first term is 9, so adjust by 0. nth term = 9n + 0
10. 8n + 11; 50th term = 411
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 19, so adjust by 11. nth term = 8n + 11
11. 7n − 2; 50th term = 348
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 5, so adjust by -2. nth term = 7n − 2
12. -3n + 13; 50th term = -137
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 10, so adjust by 13. nth term = -3n + 13
Worked examples
Find the next two terms: 5, 10, 15, 20, …
- The difference is 5.
- 20 + 5 = 25, then 30.
- Answer: 25, 30
Find the nth term of 12, 18, 24, 30, …
- Common difference 6, so start with 6n.
- 6 × 1 = 6; the first term is 12, so adjust by 6.
- nth term = 6n + 6
- Answer: 6n + 6
Find the nth term of 20, 21, 22, 23, … and the 50th term.
- Common difference 1, so start with 1n.
- 1 × 1 = 1; the first term is 20, so adjust by 19.
- nth term = 1n + 19
- Answer: 1n + 19; 50th term = 69
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 Geometric Sequences
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Frequently asked
- Is this Grade 3 Geometric Sequences 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 Quadratic Sequences, nth Term of a Linear Sequence, 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 Geometric Sequences?
- Move on to Algebraic Expressions, Equations, Inequalities, Quadratics, which build directly on this idea.
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