Exploring Sequences and Progressions
Class 9 · Mathematics
4 ideas in Class 9 Mathematics, explained in plain words, with games and quizzes to practise.
Sequences and Rules
Part of: Sequences and Rules
A sequence is an ordered list. An explicit rule uses a position number directly; a recursive rule describes a term from earlier terms.
Why it matters. A rule helps predict a term without listing every value.
Try it in two minutes
- Find the position or previous term.
- Substitute or repeat the stated operation.
- Check your result against nearby terms.
Try at home. Invent a number sequence and describe its rule.
Arithmetic Progressions
Part of: Arithmetic Progressions
An arithmetic progression has a constant difference between consecutive terms. Its nth term is a + (n−1)d, and the first n natural numbers sum to n(n+1)/2.
Why it matters. The constant difference predicts later terms and totals.
Try it in two minutes
- Find the common difference.
- Use the term number in the AP rule.
- For a natural-number sum, use n(n+1)/2.
Try at home. Look for a fixed increase or decrease in a list.
Geometric Progressions
Part of: Geometric Progressions
A geometric progression has the same ratio between consecutive terms. With first term a and common ratio r, its nth term is ar to the power n−1.
Why it matters. Repeated multiplication can make a sequence grow or shrink quickly.
Try it in two minutes
- Divide a term by the previous term.
- Check that the ratio stays the same.
- Multiply repeatedly or use the nth-term rule.
Try at home. Compare a repeated-addition pattern with repeated multiplication.
Comparing Growth Patterns
Part of: Comparing Growth Patterns
Arithmetic patterns change by repeated addition, while geometric patterns change by repeated multiplication. Their graphs and long-term growth behave differently.
Why it matters. Recognising the operation reveals how quickly a pattern changes.
Try it in two minutes
- Check differences first.
- If not constant, compare ratios.
- Use the pattern rule to predict.
Try at home. Compare two savings plans that add a fixed amount or multiply by a fixed factor.
What your child will practise
- Arithmetic Progressions: Space Quick Fire (Quick Fire)
- Comparing Growth Patterns: Desert Puzzle (Clue Puzzle)
- Geometric Progressions: Desert Quest (Flip and Match)
- Geometric Progressions: Number Quest (Match It Up)
- Sequences and Rules: Mission Control Quest (Collect the Answer)
- Quiz: Arithmetic Progressions (8 questions)
- Quiz: Comparing Growth Patterns (8 questions)
- Quiz: Geometric Progressions (8 questions)
- Quiz: Sequences and Rules (8 questions)