Algebra

Linear Sequences

Master linear sequences using the Box and Ring rule. Apply rules, find rules, and calculate any term in a sequence.

Linear Sequences
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Activity
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Questions
Summary
Activity Mode
Choose which type of sequence problem you want to practise.
📦
Apply a Rule

Given the rule, write the first 5 terms

🔍
Find a Rule

Given the sequence, find the Box and Ring

🎯
Find the nth Term

Find the rule, then calculate a specific term

Step 1 of 4
Game Mode
Play against the clock or answer a set number of questions.
Timed Challenge

Answer as many as possible

before time runs out

Fixed Questions

Answer a set number

at your own pace

Step 2 of 4
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📐 Ready to practise sequences?

Use the Box and Ring rule to solve each question.

🏆
Activity complete!
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How to play
1
Apply a Rule
You are given the nth term rule (e.g. 3n + 2) and must write the first 5 terms of the sequence.
2
Find a Rule
You are shown the first 5 terms. Find the common difference (Box) and the 0th term (Ring) to write the nth term rule.
3
Find the nth Term
You are shown the first 5 terms and a target position. First find the rule using the Box and Ring, then use it to calculate the answer.
3n + 2 → 5, 8, 11, 14, 17…
Box = 3, Ring = 2, so 3n + 2