Free Grade 3 Working with Geometric Sequences Worksheets
Free Grade 3 worksheets 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
15 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: 5, 11, 17, 23, …[1]
- 2.Find the next two terms: 6, 8, 10, 12, …[1]
- 3.Find the next two terms: 12, 16, 20, 24, …[1]
- 4.Find the next two terms: 9, 18, 27, 36, …[1]
- 5.Find the nth term of 20, 22, 24, 26, …[2]
- 6.Find the nth term of 1, -2, -5, -8, …[2]
- 7.Find the nth term of 9, 16, 23, 30, …[2]
- 8.Find the nth term of 6, 1, -4, -9, …[2]
- 9.Find the nth term of 13, 21, 29, 37, … and the 50th term.[3]
- 10.Find the nth term of 11, 17, 23, 29, … and the 50th term.[3]
- 11.Find the nth term of 3, -2, -7, -12, … and the 50th term.[3]
- 12.Find the nth term of 17, 25, 33, 41, … and the 50th term.[3]
Show answers and working
1. 29, 35
The difference is 6. 23 + 6 = 29, then 35.
2. 14, 16
The difference is 2. 12 + 2 = 14, then 16.
3. 28, 32
The difference is 4. 24 + 4 = 28, then 32.
4. 45, 54
The difference is 9. 36 + 9 = 45, then 54.
5. 2n + 18
Common difference 2, so start with 2n. 2 × 1 = 2; the first term is 20, so adjust by 18. nth term = 2n + 18
6. -3n + 4
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 1, so adjust by 4. nth term = -3n + 4
7. 7n + 2
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 9, so adjust by 2. nth term = 7n + 2
8. -5n + 11
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 6, so adjust by 11. nth term = -5n + 11
9. 8n + 5; 50th term = 405
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 13, so adjust by 5. nth term = 8n + 5
10. 6n + 5; 50th term = 305
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 11, so adjust by 5. nth term = 6n + 5
11. -5n + 8; 50th term = -242
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 3, so adjust by 8. nth term = -5n + 8
12. 8n + 9; 50th term = 409
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 17, so adjust by 9. nth term = 8n + 9
Worked examples
Find the next two terms: 5, 12, 19, 26, …
- The difference is 7.
- 26 + 7 = 33, then 40.
- Answer: 33, 40
Find the nth term of 14, 13, 12, 11, …
- Common difference -1, so start with -1n.
- -1 × 1 = -1; the first term is 14, so adjust by 15.
- nth term = -1n + 15
- Answer: -1n + 15
Find the nth term of 19, 26, 33, 40, … and the 50th term.
- Common difference 7, so start with 7n.
- 7 × 1 = 7; the first term is 19, so adjust by 12.
- nth term = 7n + 12
- Answer: 7n + 12; 50th term = 362
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 Working with Geometric Sequences
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Working with 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 Introducing Geometric Sequences, 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 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.
Related resources
Stuck on Working with Geometric Sequences? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor