Free Grade 3 nth Term of a Linear Sequence Lessons
Free Grade 3 lessons 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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30 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: 3, 8, 13, 18, …[1]
- 2.Find the next two terms: 7, 10, 13, 16, …[1]
- 3.Find the next two terms: 16, 25, 34, 43, …[1]
- 4.Find the next two terms: 11, 20, 29, 38, …[1]
- 5.Find the nth term of 16, 13, 10, 7, …[2]
- 6.Find the nth term of 8, 15, 22, 29, …[2]
- 7.Find the nth term of 6, 3, 0, -3, …[2]
- 8.Find the nth term of 17, 16, 15, 14, …[2]
- 9.Find the nth term of 10, 17, 24, 31, … and the 50th term.[3]
- 10.Find the nth term of 17, 18, 19, 20, … and the 50th term.[3]
- 11.Find the nth term of 1, -5, -11, -17, … and the 50th term.[3]
- 12.Find the nth term of 8, 12, 16, 20, … and the 50th term.[3]
Show answers and working
1. 23, 28
The difference is 5. 18 + 5 = 23, then 28.
2. 19, 22
The difference is 3. 16 + 3 = 19, then 22.
3. 52, 61
The difference is 9. 43 + 9 = 52, then 61.
4. 47, 56
The difference is 9. 38 + 9 = 47, then 56.
5. -3n + 19
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 16, so adjust by 19. nth term = -3n + 19
6. 7n + 1
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 8, so adjust by 1. nth term = 7n + 1
7. -3n + 9
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 6, so adjust by 9. nth term = -3n + 9
8. -1n + 18
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 17, so adjust by 18. nth term = -1n + 18
9. 7n + 3; 50th term = 353
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 10, so adjust by 3. nth term = 7n + 3
10. 1n + 16; 50th term = 66
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 17, so adjust by 16. nth term = 1n + 16
11. -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
12. 4n + 4; 50th term = 204
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 8, so adjust by 4. nth term = 4n + 4
Worked examples
Find the next two terms: 6, 14, 22, 30, …
- The difference is 8.
- 30 + 8 = 38, then 46.
- Answer: 38, 46
Find the nth term of 11, 16, 21, 26, …
- Common difference 5, so start with 5n.
- 5 × 1 = 5; the first term is 11, so adjust by 6.
- nth term = 5n + 6
- Answer: 5n + 6
Find the nth term of 15, 9, 3, -3, … and the 50th term.
- Common difference -6, so start with -6n.
- -6 × 1 = -6; the first term is 15, so adjust by 21.
- nth term = -6n + 21
- Answer: -6n + 21; 50th term = -279
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.
- How is the lesson sequenced?
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- What comes next after nth Term of a Linear Sequence?
- Move on to Quadratic Sequences, Geometric Sequences, Algebraic Expressions, Equations, which build directly on this idea.
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