Geometric Sequences (Intro)
A list where each term multiplies by a constant ratio.
Key idea
A list where each term multiplies by a constant ratio.
In depth
A geometric sequence multiplies by a constant ratio r each step: aₙ = a₁ rⁿ⁻¹. It grows or shrinks exponentially.
Worked example
2, 6, 18, 54, ... has r = 3; the 5th term is 2 × 3⁴ = 162.
Formula
Real-world uses
- Modelling bacteria doubling each hour or a ball bouncing back a fixed fraction of its height
Common mistake
Confusing a common difference with a common ratio.
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 Geometric Sequences (Intro)?
A list where each term multiplies by a constant ratio. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Geometric Sequences (Intro)?
The key formula is aₙ = a₁ rⁿ⁻¹.
Where is Geometric Sequences (Intro) used in real life?
Real-world examples: Modelling bacteria doubling each hour or a ball bouncing back a fixed fraction of its height.
What should I learn before Geometric Sequences (Intro)?
Make sure you are comfortable with Arithmetic Sequences (Intro), the previous topic in Arithmetic & Number Sense.
What is a common mistake with Geometric Sequences (Intro)?
Confusing a common difference with a common ratio.
How can I practise Geometric Sequences (Intro)?
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 Geometric Sequences (Intro)?
Move on to Patterns and Rules 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.