Free Grade 3 Working with nth Term of a Linear Sequence Flashcards
Free Grade 3 flashcards for Working with nth Term of a Linear Sequence: 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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25 min
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Learning objectives
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- RememberIdentify working with nth term of a linear sequence
Identify working with nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with nth term of a linear sequence
Explain working with nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with nth term of a linear sequence
Calculate working with nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with nth term of a linear sequence
Compare working with nth term of a linear sequence 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 nth Term of a Linear Sequence 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: 1, 9, 17, 25, …[1]
- 2.Find the next two terms: 8, 17, 26, 35, …[1]
- 3.Find the next two terms: 10, 13, 16, 19, …[1]
- 4.Find the next two terms: 8, 11, 14, 17, …[1]
- 5.Find the nth term of 4, 6, 8, 10, …[2]
- 6.Find the nth term of 8, 12, 16, 20, …[2]
- 7.Find the nth term of 11, 5, -1, -7, …[2]
- 8.Find the nth term of 11, 16, 21, 26, …[2]
- 9.Find the nth term of 1, 3, 5, 7, … and the 50th term.[3]
- 10.Find the nth term of 1, -5, -11, -17, … and the 50th term.[3]
- 11.Find the nth term of 13, 16, 19, 22, … and the 50th term.[3]
- 12.Find the nth term of 10, 8, 6, 4, … and the 50th term.[3]
Show answers and working
1. 33, 41
The difference is 8. 25 + 8 = 33, then 41.
2. 44, 53
The difference is 9. 35 + 9 = 44, then 53.
3. 22, 25
The difference is 3. 19 + 3 = 22, then 25.
4. 20, 23
The difference is 3. 17 + 3 = 20, then 23.
5. 2n + 2
Common difference 2, so start with 2n. 2 × 1 = 2; the first term is 4, so adjust by 2. nth term = 2n + 2
6. 4n + 4
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 8, so adjust by 4. nth term = 4n + 4
7. -6n + 17
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 11, so adjust by 17. nth term = -6n + 17
8. 5n + 6
Common difference 5, so start with 5n. 5 × 1 = 5; the first term is 11, so adjust by 6. nth term = 5n + 6
9. 2n − 1; 50th term = 99
Common difference 2, so start with 2n. 2 × 1 = 2; the first term is 1, so adjust by -1. nth term = 2n − 1
10. -6n + 7; 50th term = -293
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 1, so adjust by 7. nth term = -6n + 7
11. 3n + 10; 50th term = 160
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 13, so adjust by 10. nth term = 3n + 10
12. -2n + 12; 50th term = -88
Common difference -2, so start with -2n. -2 × 1 = -2; the first term is 10, so adjust by 12. nth term = -2n + 12
Worked examples
Find the next two terms: 5, 11, 17, 23, …
- The difference is 6.
- 23 + 6 = 29, then 35.
- Answer: 29, 35
Find the nth term of 5, 12, 19, 26, …
- Common difference 7, so start with 7n.
- 7 × 1 = 7; the first term is 5, so adjust by -2.
- nth term = 7n − 2
- Answer: 7n − 2
Find the nth term of 20, 27, 34, 41, … and the 50th term.
- Common difference 7, so start with 7n.
- 7 × 1 = 7; the first term is 20, so adjust by 13.
- nth term = 7n + 13
- Answer: 7n + 13; 50th term = 363
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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- Start with Introducing nth Term of a Linear Sequence, Term-to-term Rules. Each one has its own free lesson, worksheet and quiz.
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- Move on to nth Term of a Linear Sequence in Context, Term-to-term Rules, Quadratic Sequences, Geometric Sequences, which build directly on this idea.
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