Free Grade 3 Introducing Geometric Sequences Common Errors Flashcards
Free Grade 3 flashcards for Introducing Geometric Sequences Common Errors: 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.
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20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing geometric sequences common errors
Identify introducing geometric sequences common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing geometric sequences common errors
Explain introducing geometric sequences common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing geometric sequences common errors
Calculate introducing geometric sequences common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing geometric sequences common errors
Compare introducing geometric sequences common errors 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 Common Errors 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: 6, 13, 20, 27, …[1]
- 2.Find the next two terms: 10, 18, 26, 34, …[1]
- 3.Find the next two terms: 7, 14, 21, 28, …[1]
- 4.Find the next two terms: 17, 21, 25, 29, …[1]
- 5.Find the nth term of 8, 17, 26, 35, …[2]
- 6.Find the nth term of 6, 5, 4, 3, …[2]
- 7.Find the nth term of 9, 4, -1, -6, …[2]
- 8.Find the nth term of 1, 4, 7, 10, …[2]
- 9.Find the nth term of 15, 12, 9, 6, … and the 50th term.[3]
- 10.Find the nth term of 3, -3, -9, -15, … and the 50th term.[3]
- 11.Find the nth term of 12, 18, 24, 30, … and the 50th term.[3]
- 12.Find the nth term of 13, 7, 1, -5, … and the 50th term.[3]
Show answers and working
1. 34, 41
The difference is 7. 27 + 7 = 34, then 41.
2. 42, 50
The difference is 8. 34 + 8 = 42, then 50.
3. 35, 42
The difference is 7. 28 + 7 = 35, then 42.
4. 33, 37
The difference is 4. 29 + 4 = 33, then 37.
5. 9n − 1
Common difference 9, so start with 9n. 9 × 1 = 9; the first term is 8, so adjust by -1. nth term = 9n − 1
6. -1n + 7
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 6, so adjust by 7. nth term = -1n + 7
7. -5n + 14
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 9, so adjust by 14. nth term = -5n + 14
8. 3n − 2
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 1, so adjust by -2. nth term = 3n − 2
9. -3n + 18; 50th term = -132
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 15, so adjust by 18. nth term = -3n + 18
10. -6n + 9; 50th term = -291
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 3, so adjust by 9. nth term = -6n + 9
11. 6n + 6; 50th term = 306
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 12, so adjust by 6. nth term = 6n + 6
12. -6n + 19; 50th term = -281
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 13, so adjust by 19. nth term = -6n + 19
Worked examples
Find the next two terms: 14, 18, 22, 26, …
- The difference is 4.
- 26 + 4 = 30, then 34.
- Answer: 30, 34
Find the nth term of 17, 23, 29, 35, …
- Common difference 6, so start with 6n.
- 6 × 1 = 6; the first term is 17, so adjust by 11.
- nth term = 6n + 11
- Answer: 6n + 11
Find the nth term of 6, 14, 22, 30, … and the 50th term.
- Common difference 8, so start with 8n.
- 8 × 1 = 8; the first term is 6, so adjust by -2.
- nth term = 8n − 2
- Answer: 8n − 2; 50th term = 398
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.
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Frequently asked
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- What should a learner already know before this?
- Start with Introducing Geometric Sequences Word Problems, Introducing Geometric Sequences Techniques, Quadratic Sequences. Each one has its own free lesson, worksheet and quiz.
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- Move on to Working with Geometric Sequences, Geometric Sequences in Context, which build directly on this idea.
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