Free Grade 3 Introducing Geometric Sequences Quizzes
Free Grade 3 quizzes 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
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15 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: 14, 23, 32, 41, …[1]
- 2.Find the next two terms: 2, 6, 10, 14, …[1]
- 3.Find the next two terms: 19, 24, 29, 34, …[1]
- 4.Find the next two terms: 6, 13, 20, 27, …[1]
- 5.Find the nth term of 17, 12, 7, 2, …[2]
- 6.Find the nth term of 14, 20, 26, 32, …[2]
- 7.Find the nth term of 20, 27, 34, 41, …[2]
- 8.Find the nth term of 11, 15, 19, 23, …[2]
- 9.Find the nth term of 19, 13, 7, 1, … and the 50th term.[3]
- 10.Find the nth term of 2, 5, 8, 11, … and the 50th term.[3]
- 11.Find the nth term of 15, 18, 21, 24, … and the 50th term.[3]
- 12.Find the nth term of 2, 0, -2, -4, … and the 50th term.[3]
Show answers and working
1. 50, 59
The difference is 9. 41 + 9 = 50, then 59.
2. 18, 22
The difference is 4. 14 + 4 = 18, then 22.
3. 39, 44
The difference is 5. 34 + 5 = 39, then 44.
4. 34, 41
The difference is 7. 27 + 7 = 34, then 41.
5. -5n + 22
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 17, so adjust by 22. nth term = -5n + 22
6. 6n + 8
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 14, so adjust by 8. nth term = 6n + 8
7. 7n + 13
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 20, so adjust by 13. nth term = 7n + 13
8. 4n + 7
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 11, so adjust by 7. nth term = 4n + 7
9. -6n + 25; 50th term = -275
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 19, so adjust by 25. nth term = -6n + 25
10. 3n − 1; 50th term = 149
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 2, so adjust by -1. nth term = 3n − 1
11. 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
12. -2n + 4; 50th term = -96
Common difference -2, so start with -2n. -2 × 1 = -2; the first term is 2, so adjust by 4. nth term = -2n + 4
Worked examples
Find the next two terms: 2, 7, 12, 17, …
- The difference is 5.
- 17 + 5 = 22, then 27.
- Answer: 22, 27
Find the nth term of 13, 22, 31, 40, …
- Common difference 9, so start with 9n.
- 9 × 1 = 9; the first term is 13, so adjust by 4.
- nth term = 9n + 4
- Answer: 9n + 4
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
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Frequently asked
- Is this Grade 3 Introducing Geometric Sequences quiz really free?
- Yes. Every quizzes 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 quiz 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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