Free Grade 3 nth Term of a Linear Sequence Worksheets
Free Grade 3 worksheets for 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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15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain nth term of a linear sequence
Explain nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate nth term of a linear sequence
Calculate nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare nth term of a linear sequence
Compare nth term of a linear sequence accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify nth term of a linear sequence
Justify 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 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: 18, 21, 24, 27, …[1]
- 2.Find the next two terms: 20, 26, 32, 38, …[1]
- 3.Find the next two terms: 9, 14, 19, 24, …[1]
- 4.Find the next two terms: 18, 22, 26, 30, …[1]
- 5.Find the nth term of 13, 9, 5, 1, …[2]
- 6.Find the nth term of 20, 24, 28, 32, …[2]
- 7.Find the nth term of 15, 14, 13, 12, …[2]
- 8.Find the nth term of 18, 20, 22, 24, …[2]
- 9.Find the nth term of 6, 13, 20, 27, … and the 50th term.[3]
- 10.Find the nth term of 17, 14, 11, 8, … and the 50th term.[3]
- 11.Find the nth term of 3, -2, -7, -12, … and the 50th term.[3]
- 12.Find the nth term of 8, 15, 22, 29, … and the 50th term.[3]
Show answers and working
1. 30, 33
The difference is 3. 27 + 3 = 30, then 33.
2. 44, 50
The difference is 6. 38 + 6 = 44, then 50.
3. 29, 34
The difference is 5. 24 + 5 = 29, then 34.
4. 34, 38
The difference is 4. 30 + 4 = 34, then 38.
5. -4n + 17
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 13, so adjust by 17. nth term = -4n + 17
6. 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
7. -1n + 16
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 15, so adjust by 16. nth term = -1n + 16
8. 2n + 16
Common difference 2, so start with 2n. 2 × 1 = 2; the first term is 18, so adjust by 16. nth term = 2n + 16
9. 7n − 1; 50th term = 349
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 6, so adjust by -1. nth term = 7n − 1
10. -3n + 20; 50th term = -130
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 17, so adjust by 20. nth term = -3n + 20
11. -5n + 8; 50th term = -242
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 3, so adjust by 8. nth term = -5n + 8
12. 7n + 1; 50th term = 351
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 8, so adjust by 1. nth term = 7n + 1
Worked examples
Find the next two terms: 18, 23, 28, 33, …
- The difference is 5.
- 33 + 5 = 38, then 43.
- Answer: 38, 43
Find the nth term of 6, 2, -2, -6, …
- Common difference -4, so start with -4n.
- -4 × 1 = -4; the first term is 6, so adjust by 10.
- nth term = -4n + 10
- Answer: -4n + 10
Find the nth term of 11, 17, 23, 29, … and the 50th term.
- Common difference 6, so start with 6n.
- 6 × 1 = 6; the first term is 11, so adjust by 5.
- nth term = 6n + 5
- Answer: 6n + 5; 50th term = 305
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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- What should a learner already know before this?
- Start with Term-to-term Rules, Inequalities. Each one has its own free lesson, worksheet and quiz.
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- Move on to Quadratic Sequences, Geometric Sequences, Algebraic Expressions, Equations, which build directly on this idea.
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