Fibonacci Numbers
Each term is the sum of the two before it.
Key idea
Each term is the sum of the two before it.
In depth
Each Fibonacci number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, ... Ratios of consecutive terms approach the golden ratio 1.618. The sequence appears in spirals, branching, and counting problems.
Worked example
After 8 and 13 comes 21 and then 34.
Formula
Real-world uses
- Modelling rabbit population puzzles
- Spotting spirals in sunflowers and pine cones
- Computer algorithms
Common mistake
Starting the sequence with the wrong first two terms.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Fibonacci Numbers?
Each term is the sum of the two before it. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Fibonacci Numbers?
The key formula is Fₙ = Fₙ₋₁ + Fₙ₋₂.
Where is Fibonacci Numbers used in real life?
Real-world examples: Modelling rabbit population puzzles; Spotting spirals in sunflowers and pine cones; Computer algorithms.
What should I learn before Fibonacci Numbers?
Make sure you are comfortable with Patterns and Rules, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Fibonacci Numbers?
Starting the sequence with the wrong first two terms.
How can I practise Fibonacci Numbers?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Fibonacci Numbers?
Move on to Pascal’s Triangle Basics next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.