Free Grade 3 Geometric Sequences Lessons
Free Grade 3 lessons 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
35 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: 3, 11, 19, 27, …[1]
- 2.Find the next two terms: 19, 21, 23, 25, …[1]
- 3.Find the next two terms: 11, 17, 23, 29, …[1]
- 4.Find the next two terms: 1, 9, 17, 25, …[1]
- 5.Find the nth term of 15, 13, 11, 9, …[2]
- 6.Find the nth term of 16, 23, 30, 37, …[2]
- 7.Find the nth term of 5, 11, 17, 23, …[2]
- 8.Find the nth term of 10, 15, 20, 25, …[2]
- 9.Find the nth term of 3, 5, 7, 9, … and the 50th term.[3]
- 10.Find the nth term of 18, 24, 30, 36, … and the 50th term.[3]
- 11.Find the nth term of 10, 18, 26, 34, … and the 50th term.[3]
- 12.Find the nth term of 7, 16, 25, 34, … and the 50th term.[3]
Show answers and working
1. 35, 43
The difference is 8. 27 + 8 = 35, then 43.
2. 27, 29
The difference is 2. 25 + 2 = 27, then 29.
3. 35, 41
The difference is 6. 29 + 6 = 35, then 41.
4. 33, 41
The difference is 8. 25 + 8 = 33, then 41.
5. -2n + 17
Common difference -2, so start with -2n. -2 × 1 = -2; the first term is 15, so adjust by 17. nth term = -2n + 17
6. 7n + 9
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 16, so adjust by 9. nth term = 7n + 9
7. 6n − 1
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 5, so adjust by -1. nth term = 6n − 1
8. 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
9. 2n + 1; 50th term = 101
Common difference 2, so start with 2n. 2 × 1 = 2; the first term is 3, so adjust by 1. nth term = 2n + 1
10. 6n + 12; 50th term = 312
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 18, so adjust by 12. nth term = 6n + 12
11. 8n + 2; 50th term = 402
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 10, so adjust by 2. nth term = 8n + 2
12. 9n − 2; 50th term = 448
Common difference 9, so start with 9n. 9 × 1 = 9; the first term is 7, so adjust by -2. nth term = 9n − 2
Worked examples
Find the next two terms: 5, 13, 21, 29, …
- The difference is 8.
- 29 + 8 = 37, then 45.
- Answer: 37, 45
Find the nth term of 10, 13, 16, 19, …
- Common difference 3, so start with 3n.
- 3 × 1 = 3; the first term is 10, so adjust by 7.
- nth term = 3n + 7
- Answer: 3n + 7
Find the nth term of 16, 11, 6, 1, … and the 50th term.
- 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; 50th term = -229
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
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 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 Quadratic Sequences, nth Term of a Linear Sequence, Inequalities. 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 Geometric Sequences?
- Move on to Algebraic Expressions, Equations, Inequalities, Quadratics, which build directly on this idea.
Related resources
Stuck on Geometric Sequences? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor