Free Grade 3 nth Term of a Linear Sequence in Context Lesson Plans
Free Grade 3 lesson plans 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
25 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: 18, 26, 34, 42, …[1]
- 2.Find the next two terms: 16, 22, 28, 34, …[1]
- 3.Find the next two terms: 17, 20, 23, 26, …[1]
- 4.Find the next two terms: 18, 20, 22, 24, …[1]
- 5.Find the nth term of 4, 12, 20, 28, …[2]
- 6.Find the nth term of 14, 17, 20, 23, …[2]
- 7.Find the nth term of 7, 11, 15, 19, …[2]
- 8.Find the nth term of 10, 13, 16, 19, …[2]
- 9.Find the nth term of 4, 11, 18, 25, … and the 50th term.[3]
- 10.Find the nth term of 10, 17, 24, 31, … and the 50th term.[3]
- 11.Find the nth term of 16, 17, 18, 19, … and the 50th term.[3]
- 12.Find the nth term of 11, 16, 21, 26, … and the 50th term.[3]
Show answers and working
1. 50, 58
The difference is 8. 42 + 8 = 50, then 58.
2. 40, 46
The difference is 6. 34 + 6 = 40, then 46.
3. 29, 32
The difference is 3. 26 + 3 = 29, then 32.
4. 26, 28
The difference is 2. 24 + 2 = 26, then 28.
5. 8n − 4
Common difference 8, so start with 8n. 8 × 1 = 8; the first term is 4, so adjust by -4. nth term = 8n − 4
6. 3n + 11
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 14, so adjust by 11. nth term = 3n + 11
7. 4n + 3
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 7, so adjust by 3. nth term = 4n + 3
8. 3n + 7
Common difference 3, so start with 3n. 3 × 1 = 3; the first term is 10, so adjust by 7. nth term = 3n + 7
9. 7n − 3; 50th term = 347
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 4, so adjust by -3. nth term = 7n − 3
10. 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
11. 1n + 15; 50th term = 65
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 16, so adjust by 15. nth term = 1n + 15
12. 5n + 6; 50th term = 256
Common difference 5, so start with 5n. 5 × 1 = 5; the first term is 11, so adjust by 6. nth term = 5n + 6
Worked examples
Find the next two terms: 16, 19, 22, 25, …
- The difference is 3.
- 25 + 3 = 28, then 31.
- Answer: 28, 31
Find the nth term of 15, 18, 21, 24, …
- Common difference 3, so start with 3n.
- 3 × 1 = 3; the first term is 15, so adjust by 12.
- nth term = 3n + 12
- Answer: 3n + 12
Find the nth term of 13, 21, 29, 37, … and the 50th term.
- Common difference 8, so start with 8n.
- 8 × 1 = 8; the first term is 13, so adjust by 5.
- nth term = 8n + 5
- Answer: 8n + 5; 50th term = 405
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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- 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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