Simple Sequences
Numbers and letters always follow a secret rule — find it.
What You'll Learn
Let's Understand It Simply
A sequence is just a pattern wearing a number costume.
A sequence is an ordered list of numbers, letters, or symbols that follow a consistent rule from one term to the next. Solving a sequence means figuring out that hidden rule so you can predict any future term — even one far beyond what's shown.
The two most common rule types are arithmetic (add or subtract the same amount each time, like 3, 6, 9, 12) and geometric (multiply or divide by the same amount each time, like 2, 4, 8, 16). Learning to quickly test both types is the fastest way to crack most sequences.
Letter sequences work the same way, but you convert letters to their alphabet position first (A=1, B=2, C=3...) to reveal the numeric pattern hiding underneath.
Think of a sequence like footprints in the sand. Each footprint (term) is placed a consistent distance and direction from the last one. If you measure just two footprints carefully, you can predict exactly where footprint number 20 would be — without walking there yourself.
Visual Explanation
See how each term connects to the next through one consistent rule.
5 rounds · 12s each · find what comes next before time runs out
Test your pattern recognition speed with 5 rapid-fire number sequences. Can you spot the rule before the clock runs out?
Worked Examples
The gap between terms isn't constant (5, 10, 20 differ by different amounts), so this probably isn't arithmetic — let me check for multiplication.
When differences aren't constant, always test ratios (division) next — many sequences are multiplicative rather than additive.
Interactive Activity
Beat the clock finding the rule behind rapid-fire number sequences.
5 rounds · 12s each · find what comes next before time runs out
Test your pattern recognition speed with 5 rapid-fire number sequences. Can you spot the rule before the clock runs out?
Common Mistakes to Avoid
Students often think: Only checking addition/subtraction and giving up if it doesn't fit.
Why it's wrong: Many sequences use multiplication, division, or even a two-term dependency (like Fibonacci).
Correct thinking: If differences aren't constant, test ratios next, then check if terms depend on two previous terms.
Students often think: Forgetting to convert letters to numbers before searching for the pattern.
Why it's wrong: It's much harder to spot numeric relationships directly between letters.
Correct thinking: Always convert letters to their alphabet position (A=1, B=2...) first.
Students often think: Assuming a sequence rule from only 2 terms.
Why it's wrong: Two terms can accidentally fit many different rules.
Correct thinking: Confirm your rule works for at least 3-4 consecutive terms before trusting it.
Real-World Applications
Finance
Compound interest follows a geometric sequence — money multiplies by a fixed ratio each period.
Nature
Flower petals and pinecones often follow the Fibonacci sequence for optimal growth efficiency.
Computer Science
Algorithms analyze sequences to detect patterns in data, from stock prices to network traffic.
Music Theory
Musical scales and chord progressions follow structured numeric sequences.
Memory Tricks
🧠 Add, Then Multiply
Always test in this order: 1) constant difference (addition), 2) constant ratio (multiplication), 3) two-term dependency (Fibonacci-style).
🧠 Letters Are Secretly Numbers
Whenever you see a letter sequence, immediately relabel it with numbers (A=1, B=2...) before doing anything else.
Quick Revision Infographic
Simple Sequences
Mini Quiz
Question 1 / 53, 9, 27, 81, ? — what comes next?
A sequence alternates between two separate rules: 2, 100, 4, 90, 6, 80, 8, ? — find the next term.
Key Takeaways
Ready to complete this chapter?
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