Lesson 1 — Sequences & Series
Start by doing the thing yourself — no explanation yet. Look at each pattern and pick the number you think comes next.
This activity needs JavaScript enabled. The lesson below still covers everything.
What you just did
You found the rule that turns one term into the next. That is the whole idea of a sequence: an ordered list of numbers where each one follows from a rule. Each number is a term.
Two kinds of rule show up over and over in elementary math:
- Arithmetic sequence — you add the same number each time. That fixed number is the common difference. Example: 2, 5, 8, 11, … adds 3 every step.
- Geometric sequence — you multiply by the same number each time. That fixed number is the common ratio. Example: 3, 6, 12, 24, … multiplies by 2 every step.
The quickest test: look at how you get from one term to the next. If you keep adding the same amount, it is arithmetic. If you keep multiplying by the same amount, it is geometric.
Arithmetic or geometric? You decide
For each sequence below, decide whether the rule is "add the same amount" (arithmetic) or "multiply by the same amount" (geometric). Instant feedback — guessing is how you learn the pattern.
This activity needs JavaScript enabled. The lesson below still covers everything.
From sequence to series
A series is what you get when you add up the terms of a sequence. "1, 2, 3, 4" is a sequence; "1 + 2 + 3 + 4 = 10" is the matching series.
For an arithmetic series you do not have to add term by term. There is a shortcut a young Carl Friedrich Gauss famously spotted: pair the first term with the last, the second with the second-to-last, and so on — every pair has the same total. So:
For 1 + 2 + 3 + … + 100: that is 100 × (1 + 100) ÷ 2 = 100 × 101 ÷ 2 = 5050.
You will not always need the formula in EC-6 work, but the reasoning — pairing terms so the adding becomes easy — is exactly the kind of number sense the exam rewards.
Why this matters in the classroom
Patterns are where young students first meet algebra. "What comes next, and how do you know?" is a sequence question. Asking a child to describe the rule in words ("it goes up by 2 each time") builds the habit of generalising — the seed of writing an expression like 2n later on.
Quick check
This activity needs JavaScript enabled.