Linear Sequences
This topic covers 5 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Spot the Pattern
Identify the common difference in a sequence - Continue the Sequence
Find the next terms using the rule - Find the nth Term Rule
Write the rule for the nth term - Use the nth Term
Find any term using the formula - Challenge — Sequence Problems
Complex sequence problems including reverse questions
Common Mistakes
- Confusing the difference between terms with the terms themselves (e.g. for the sequence 3, 7, 11, 15 — saying the rule is "4" instead of "add 4 each time" or "start at 3, add 4")
A sequence rule needs both a starting number and a step: "Start at 3, add 4 each time." The difference alone is not enough — many sequences can have the same difference but start at different numbers. - Making errors finding the nth term because of confusion between the term number and the term value
The "term number" is its POSITION (1st, 2nd, 3rd...) and the "term value" is the actual number. For the sequence 5, 8, 11, 14 — the 3rd term (position 3) has a value of 11. Make a table with columns for position and value.
Tips for Parents
- Find sequences in real life: house numbers on one side of the street (2, 4, 6, 8...), the number of legs on groups of chairs.
- Ask your child to continue sequences: "3, 7, 11, 15, ... What comes next? What is the rule?" Then try making sequences backwards.
- Draw sequences using matchstick patterns: "Shape 1 uses 3 matchsticks, shape 2 uses 5, shape 3 uses 7... How many for shape 10?"
- Make a table of position and value. Ask: "Can you see a shortcut to find the 100th term without working out all 100?"
Key Words
- Sequence — A list of numbers that follows a pattern — like 2, 5, 8, 11, 14...
- Term — Each number in a sequence — 8 is the third term of the sequence 2, 5, 8, 11.
- Rule — The pattern that generates the sequence — "start at 2, add 3 each time."
- Linear sequence — A sequence where the same number is added each time — the differences are constant.
- nth term — A formula that lets you find any term without listing them all — for the sequence 3, 5, 7, 9, the nth term is 2n + 1.
Where This Fits
Before this topic: Children should understand patterns, skip counting, and be comfortable with addition and multiplication.
After this topic: Linear sequences lead to finding nth term formulas, quadratic sequences, and algebraic expressions in secondary school.
How MathCraft Teaches This
In MathCraft, Linear Sequences is taught through the Algebra & Arithmetic adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 5 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Linear Sequences with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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