Free Grade 3 Working with nth Term of a Linear Sequence Worksheets
Free Grade 3 worksheets 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.
Free
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- 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: 9, 15, 21, 27, …[1]
- 2.Find the next two terms: 18, 24, 30, 36, …[1]
- 3.Find the next two terms: 19, 27, 35, 43, …[1]
- 4.Find the next two terms: 11, 20, 29, 38, …[1]
- 5.Find the nth term of 15, 11, 7, 3, …[2]
- 6.Find the nth term of 12, 14, 16, 18, …[2]
- 7.Find the nth term of 3, 1, -1, -3, …[2]
- 8.Find the nth term of 7, 8, 9, 10, …[2]
- 9.Find the nth term of 19, 23, 27, 31, … and the 50th term.[3]
- 10.Find the nth term of 10, 9, 8, 7, … and the 50th term.[3]
- 11.Find the nth term of 9, 8, 7, 6, … 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, 39
The difference is 6. 27 + 6 = 33, then 39.
2. 42, 48
The difference is 6. 36 + 6 = 42, then 48.
3. 51, 59
The difference is 8. 43 + 8 = 51, then 59.
4. 47, 56
The difference is 9. 38 + 9 = 47, then 56.
5. -4n + 19
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 15, so adjust by 19. nth term = -4n + 19
6. 2n + 10
Common difference 2, so start with 2n. 2 × 1 = 2; the first term is 12, so adjust by 10. nth term = 2n + 10
7. -2n + 5
Common difference -2, so start with -2n. -2 × 1 = -2; the first term is 3, so adjust by 5. nth term = -2n + 5
8. 1n + 6
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 7, so adjust by 6. nth term = 1n + 6
9. 4n + 15; 50th term = 215
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 19, so adjust by 15. nth term = 4n + 15
10. -1n + 11; 50th term = -39
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 10, so adjust by 11. nth term = -1n + 11
11. -1n + 10; 50th term = -40
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 9, so adjust by 10. nth term = -1n + 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: 14, 20, 26, 32, …
- The difference is 6.
- 32 + 6 = 38, then 44.
- Answer: 38, 44
Find the nth term of 15, 12, 9, 6, …
- Common difference -3, so start with -3n.
- -3 × 1 = -3; the first term is 15, so adjust by 18.
- nth term = -3n + 18
- Answer: -3n + 18
Find the nth term of 17, 12, 7, 2, … and the 50th term.
- Common difference -5, so start with -5n.
- -5 × 1 = -5; the first term is 17, so adjust by 22.
- nth term = -5n + 22
- Answer: -5n + 22; 50th term = -228
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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- What should a learner already know before this?
- 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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- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with nth Term of a Linear Sequence?
- 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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