Free Grade 3 nth Term of a Linear Sequence in Context Lessons
Free Grade 3 lessons for nth Term of a Linear Sequence in Context: 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
Core
20 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 in context
Explain nth term of a linear sequence in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate nth term of a linear sequence in context
Calculate nth term of a linear sequence in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare nth term of a linear sequence in context
Compare nth term of a linear sequence in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify nth term of a linear sequence in context
Justify nth term of a linear sequence in context 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 in Context 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: 15, 23, 31, 39, …[1]
- 2.Find the next two terms: 19, 22, 25, 28, …[1]
- 3.Find the next two terms: 3, 8, 13, 18, …[1]
- 4.Find the next two terms: 2, 4, 6, 8, …[1]
- 5.Find the nth term of 6, 5, 4, 3, …[2]
- 6.Find the nth term of 12, 16, 20, 24, …[2]
- 7.Find the nth term of 19, 20, 21, 22, …[2]
- 8.Find the nth term of 5, 10, 15, 20, …[2]
- 9.Find the nth term of 10, 7, 4, 1, … and the 50th term.[3]
- 10.Find the nth term of 15, 17, 19, 21, … and the 50th term.[3]
- 11.Find the nth term of 17, 16, 15, 14, … and the 50th term.[3]
- 12.Find the nth term of 3, 4, 5, 6, … and the 50th term.[3]
Show answers and working
1. 47, 55
The difference is 8. 39 + 8 = 47, then 55.
2. 31, 34
The difference is 3. 28 + 3 = 31, then 34.
3. 23, 28
The difference is 5. 18 + 5 = 23, then 28.
4. 10, 12
The difference is 2. 8 + 2 = 10, then 12.
5. -1n + 7
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 6, so adjust by 7. nth term = -1n + 7
6. 4n + 8
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 12, so adjust by 8. nth term = 4n + 8
7. 1n + 18
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 19, so adjust by 18. nth term = 1n + 18
8. 5n + 0
Common difference 5, so start with 5n. 5 × 1 = 5; the first term is 5, so adjust by 0. nth term = 5n + 0
9. -3n + 13; 50th term = -137
Common difference -3, so start with -3n. -3 × 1 = -3; the first term is 10, so adjust by 13. nth term = -3n + 13
10. 2n + 13; 50th term = 113
Common difference 2, so start with 2n. 2 × 1 = 2; the first term is 15, so adjust by 13. nth term = 2n + 13
11. -1n + 18; 50th term = -32
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 17, so adjust by 18. nth term = -1n + 18
12. 1n + 2; 50th term = 52
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 3, so adjust by 2. nth term = 1n + 2
Worked examples
Find the next two terms: 1, 4, 7, 10, …
- The difference is 3.
- 10 + 3 = 13, then 16.
- Answer: 13, 16
Find the nth term of 15, 20, 25, 30, …
- Common difference 5, so start with 5n.
- 5 × 1 = 5; the first term is 15, so adjust by 10.
- nth term = 5n + 10
- Answer: 5n + 10
Find the nth term of 10, 19, 28, 37, … and the 50th term.
- Common difference 9, so start with 9n.
- 9 × 1 = 9; the first term is 10, so adjust by 1.
- nth term = 9n + 1
- Answer: 9n + 1; 50th term = 451
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 Working with nth Term of a Linear Sequence, 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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- What comes next after nth Term of a Linear Sequence in Context?
- Move on to Term-to-term Rules, Quadratic Sequences, Geometric Sequences, which build directly on this idea.
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