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🔢 Number Patterns and Sequences

Spot the rule behind number sequences - even ones with decimal steps or that dip below zero - then build patterns from two rules and graph how they relate.

lessons

~20 min

to learn

🔢 Math

subject

Ages 6–12

level

Start the course →

What you’ll learn

Spotting the RuleFind and use the term-to-term rule of a linear sequence, including decimal steps.The gap between terms reveals the rule. In 2.5, 4.0, 5.5, ... each step adds 1.5, so the next term is 7.0. Checking two gaps confirms the rule is constant. Some rules add and some subtract - matching a sequence to its rule is the key skill.
Sequences That Cross ZeroGenerate linear sequences that cross zero into negative terms.A subtracting rule doesn't stop at zero. The sequence 3, 1, -1, -3, ... keeps subtracting 2 straight through zero, continuing to -5 and -7. The rule stays the same; only the numbers change sign. A number line makes the crossing easy to see.
Two Patterns TogetherGenerate two sequences from two rules, relate corresponding terms, and form ordered pairs to plot.Starting both at 0, 'add 3' gives 0, 3, 6, 9 and 'add 6' gives 0, 6, 12, 18 - each add-6 term is double its partner. Pairing corresponding terms makes ordered pairs like (3, 6) and (9, 18), which plot as a straight line because the doubling is constant.

Questions this course answers

What happens to a 'subtract 2' rule when it reaches zero?

The rule keeps going past zero into negatives.

Two sequences start at 0: one adds 3, one adds 6. How do matching terms relate?

Add-6 grows twice as fast, so its terms are double.

When you plot the ordered pairs (3,6), (6,12), (9,18), the points...

A constant doubling makes a straight line.

Grounded in trusted sources

Khan Academy
BBC Bitesize - Maths
NRICH - University of Cambridge
Math is Fun

Every Wunder lesson is built from real, reputable sources — never invented.

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