Free Grade 3 nth Term of a Linear Sequence Lesson Plans
Free Grade 3 lesson plans 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.
Free
Core
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: 7, 9, 11, 13, …[1]
- 2.Find the next two terms: 15, 21, 27, 33, …[1]
- 3.Find the next two terms: 19, 25, 31, 37, …[1]
- 4.Find the next two terms: 1, 10, 19, 28, …[1]
- 5.Find the nth term of 19, 15, 11, 7, …[2]
- 6.Find the nth term of 20, 19, 18, 17, …[2]
- 7.Find the nth term of 14, 23, 32, 41, …[2]
- 8.Find the nth term of 4, 13, 22, 31, …[2]
- 9.Find the nth term of 4, -1, -6, -11, … and the 50th term.[3]
- 10.Find the nth term of 2, 1, 0, -1, … and the 50th term.[3]
- 11.Find the nth term of 12, 7, 2, -3, … and the 50th term.[3]
- 12.Find the nth term of 2, -4, -10, -16, … and the 50th term.[3]
Show answers and working
1. 15, 17
The difference is 2. 13 + 2 = 15, then 17.
2. 39, 45
The difference is 6. 33 + 6 = 39, then 45.
3. 43, 49
The difference is 6. 37 + 6 = 43, then 49.
4. 37, 46
The difference is 9. 28 + 9 = 37, then 46.
5. -4n + 23
Common difference -4, so start with -4n. -4 × 1 = -4; the first term is 19, so adjust by 23. nth term = -4n + 23
6. -1n + 21
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 20, so adjust by 21. nth term = -1n + 21
7. 9n + 5
Common difference 9, so start with 9n. 9 × 1 = 9; the first term is 14, so adjust by 5. nth term = 9n + 5
8. 9n − 5
Common difference 9, so start with 9n. 9 × 1 = 9; the first term is 4, so adjust by -5. nth term = 9n − 5
9. -5n + 9; 50th term = -241
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 4, so adjust by 9. nth term = -5n + 9
10. -1n + 3; 50th term = -47
Common difference -1, so start with -1n. -1 × 1 = -1; the first term is 2, so adjust by 3. nth term = -1n + 3
11. -5n + 17; 50th term = -233
Common difference -5, so start with -5n. -5 × 1 = -5; the first term is 12, so adjust by 17. nth term = -5n + 17
12. -6n + 8; 50th term = -292
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 2, so adjust by 8. nth term = -6n + 8
Worked examples
Find the next two terms: 19, 24, 29, 34, …
- The difference is 5.
- 34 + 5 = 39, then 44.
- Answer: 39, 44
Find the nth term of 5, 3, 1, -1, …
- Common difference -2, so start with -2n.
- -2 × 1 = -2; the first term is 5, so adjust by 7.
- nth term = -2n + 7
- Answer: -2n + 7
Find the nth term of 6, 9, 12, 15, … and the 50th term.
- Common difference 3, so start with 3n.
- 3 × 1 = 3; the first term is 6, so adjust by 3.
- nth term = 3n + 3
- Answer: 3n + 3; 50th term = 153
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
How mastery is evidenced, and which standards it maps to.
Every free resource for nth Term of a Linear Sequence
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 nth Term of a Linear Sequence lesson plan really free?
- Yes. Every lesson plans on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- 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 plan sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- 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.
Related resources
Stuck on nth Term of a Linear Sequence? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor