Free Grade 3 Introducing nth Term of a Linear Sequence Worksheets
Free Grade 3 worksheets for Introducing 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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Higher
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing nth term of a linear sequence
Identify introducing nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing nth term of a linear sequence
Explain introducing nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing nth term of a linear sequence
Calculate introducing nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing nth term of a linear sequence
Compare introducing 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 Introducing 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: 10, 17, 24, 31, …[1]
- 2.Find the next two terms: 14, 22, 30, 38, …[1]
- 3.Find the next two terms: 5, 9, 13, 17, …[1]
- 4.Find the next two terms: 9, 16, 23, 30, …[1]
- 5.Find the nth term of 13, 19, 25, 31, …[2]
- 6.Find the nth term of 1, -5, -11, -17, …[2]
- 7.Find the nth term of 20, 24, 28, 32, …[2]
- 8.Find the nth term of 11, 10, 9, 8, …[2]
- 9.Find the nth term of 7, 10, 13, 16, … and the 50th term.[3]
- 10.Find the nth term of 1, 5, 9, 13, … and the 50th term.[3]
- 11.Find the nth term of 12, 11, 10, 9, … and the 50th term.[3]
- 12.Find the nth term of 2, 5, 8, 11, … and the 50th term.[3]
Show answers and working
1. 38, 45
The difference is 7. 31 + 7 = 38, then 45.
2. 46, 54
The difference is 8. 38 + 8 = 46, then 54.
3. 21, 25
The difference is 4. 17 + 4 = 21, then 25.
4. 37, 44
The difference is 7. 30 + 7 = 37, then 44.
5. 6n + 7
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 13, so adjust by 7. nth term = 6n + 7
6. -6n + 7
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 1, so adjust by 7. nth term = -6n + 7
7. 4n + 16
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 20, so adjust by 16. nth term = 4n + 16
8. -1n + 12
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 11, so adjust by 12. nth term = -1n + 12
9. 3n + 4; 50th term = 154
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 7, so adjust by 4. nth term = 3n + 4
10. 4n − 3; 50th term = 197
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 1, so adjust by -3. nth term = 4n − 3
11. -1n + 13; 50th term = -37
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 12, so adjust by 13. nth term = -1n + 13
12. 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
Worked examples
Find the next two terms: 17, 23, 29, 35, …
- The difference is 6.
- 35 + 6 = 41, then 47.
- Answer: 41, 47
Find the nth term of 3, 7, 11, 15, …
- Common difference 4, so start with 4n.
- 4 × 1 = 4; the first term is 3, so adjust by -1.
- nth term = 4n − 1
- Answer: 4n − 1
Find the nth term of 9, 13, 17, 21, … and the 50th term.
- Common difference 4, so start with 4n.
- 4 × 1 = 4; the first term is 9, so adjust by 5.
- nth term = 4n + 5
- Answer: 4n + 5; 50th term = 205
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 Term-to-term Rules. Each one has its own free lesson, worksheet and quiz.
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- Move on to Working with nth Term of a Linear Sequence, nth Term of a Linear Sequence in Context, Term-to-term Rules, Quadratic Sequences, which build directly on this idea.
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