Patterns in Mathematics: Solving Pattern-Based Questions: quick revision, 15 bites

Every Pattern Hides a Rule

Find the rule, crack the pattern.

A pattern is not random — it is a **sequence generated by a fixed rule**. Your job in any pattern question is to discover that rule.

Takeaway. Never guess the next term — first state the rule that produces every term.

Terms, Rule, and Sequence

Three words every pattern question uses.

Takeaway. A sequence is the visible output; the rule is the hidden engine.

4-Step Method to Solve Any Pattern

Four steps beat random guessing.

Takeaway. Differences first, ratios second — that solves most school-level pattern questions.

Arithmetic vs Geometric Patterns

Add or multiply — know the difference.

Takeaway. Constant difference → arithmetic; constant ratio → geometric.

nth Term of an Arithmetic Pattern

Jump to any term without listing all.

Takeaway. The nth-term formula turns any arithmetic pattern into a one-line calculation.

nth Term of a Geometric Pattern

Multiply your way to term 100.

Takeaway. Geometric patterns grow by powers of r — the exponent is always n−1.

Don't Assume the First Rule You See

One match isn't proof.

Takeaway. Verify the rule against all given terms before predicting.

D-A-R: The Pattern Check Order

Difference, then ratio, then squares.

Takeaway. D-A-R keeps your pattern-checking systematic and fast.

Square-Number Pattern in Disguise

1, 4, 9, 16 — see the squares?

Takeaway. If differences grow by a constant amount, suspect a square or quadratic pattern.

Alternating Pattern: Two Rules in One

Two rules, one sequence.

Takeaway. When a single rule fails, split the sequence into odd and even positions.

Test the Rule Backwards

Run the rule in reverse.

Takeaway. A rule that reproduces every given term is almost certainly correct.

Patterns Power Real Predictions

Patterns run your world quietly.

Takeaway. Recognising patterns is how we predict growth, cost, and change.

Exam Shortcut: Write Differences in a Row

Stack the differences, spot the rule.

Takeaway. A visible difference row is the fastest route to the rule under exam pressure.

Beware the 'Obvious' Next Term

Many answers fit — pick the simplest.

Takeaway. Occam's razor applies: simplest consistent rule wins.

The Fibonacci Pattern in Nature

Nature's favourite sequence.

The **Fibonacci sequence** (1, 1, 2, 3, 5, 8, 13, …) follows the rule *each term = sum of the previous two*. It appears in pinecones, sunflowers, and nautilus shells.

Takeaway. Fibonacci is the classic example of a rule that builds each term from the previous ones.