Free Grade 3 Introducing Geometric Sequences Worksheets
Free Grade 3 worksheets for Introducing 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
Higher
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing geometric sequences
Identify introducing geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing geometric sequences
Explain introducing geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing geometric sequences
Calculate introducing geometric sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing geometric sequences
Compare introducing 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 Introducing 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: 9, 12, 15, 18, …[1]
- 2.Find the next two terms: 8, 16, 24, 32, …[1]
- 3.Find the next two terms: 1, 10, 19, 28, …[1]
- 4.Find the next two terms: 3, 12, 21, 30, …[1]
- 5.Find the nth term of 5, 7, 9, 11, …[2]
- 6.Find the nth term of 15, 14, 13, 12, …[2]
- 7.Find the nth term of 18, 17, 16, 15, …[2]
- 8.Find the nth term of 9, 10, 11, 12, …[2]
- 9.Find the nth term of 3, 11, 19, 27, … and the 50th term.[3]
- 10.Find the nth term of 2, -2, -6, -10, … and the 50th term.[3]
- 11.Find the nth term of 18, 15, 12, 9, … and the 50th term.[3]
- 12.Find the nth term of 15, 18, 21, 24, … and the 50th term.[3]
Show answers and working
1. 21, 24
The difference is 3. 18 + 3 = 21, then 24.
2. 40, 48
The difference is 8. 32 + 8 = 40, then 48.
3. 37, 46
The difference is 9. 28 + 9 = 37, then 46.
4. 39, 48
The difference is 9. 30 + 9 = 39, then 48.
5. 2n + 3
Common difference 2, so start with 2n. 2 × 1 = 2; the first term is 5, so adjust by 3. nth term = 2n + 3
6. -1n + 16
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 15, so adjust by 16. nth term = -1n + 16
7. -1n + 19
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 18, so adjust by 19. nth term = -1n + 19
8. 1n + 8
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 9, so adjust by 8. nth term = 1n + 8
9. 8n − 5; 50th term = 395
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 3, so adjust by -5. nth term = 8n − 5
10. -4n + 6; 50th term = -194
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 2, so adjust by 6. nth term = -4n + 6
11. -3n + 21; 50th term = -129
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 18, so adjust by 21. nth term = -3n + 21
12. 3n + 12; 50th term = 162
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 15, so adjust by 12. nth term = 3n + 12
Worked examples
Find the next two terms: 11, 20, 29, 38, …
- The difference is 9.
- 38 + 9 = 47, then 56.
- Answer: 47, 56
Find the nth term of 17, 21, 25, 29, …
- Common difference 4, so start with 4n.
- 4 × 1 = 4; the first term is 17, so adjust by 13.
- nth term = 4n + 13
- Answer: 4n + 13
Find the nth term of 9, 3, -3, -9, … and the 50th term.
- Common difference -6, so start with -6n.
- -6 × 1 = -6; the first term is 9, so adjust by 15.
- nth term = -6n + 15
- Answer: -6n + 15; 50th term = -285
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 Introducing 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. 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 Introducing Geometric Sequences?
- Move on to Working with Geometric Sequences, Geometric Sequences in Context, Term-to-term Rules, nth Term of a Linear Sequence, which build directly on this idea.
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