Arithmetic Sequences (Intro)
A list where each term adds a constant difference.
Key idea
A list where each term adds a constant difference.
In depth
An arithmetic sequence has a constant difference d between consecutive terms: aₙ = a₁ + (n−1)d. The graph of terms against n is a straight line.
Worked example
3, 7, 11, 15, ... has d = 4; the 10th term is 3 + 9×4 = 39.
Formula
Real-world uses
- Calculating savings that grow by a fixed amount each month
- Planning evenly spaced seating or shelving
Common mistake
Using n×d instead of (n−1)×d, shifting the answer by one step.
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 Arithmetic Sequences (Intro)?
A list where each term adds a constant difference. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Arithmetic Sequences (Intro)?
The key formula is aₙ = a₁ + (n−1)d.
Where is Arithmetic Sequences (Intro) used in real life?
Real-world examples: Calculating savings that grow by a fixed amount each month; Planning evenly spaced seating or shelving.
What should I learn before Arithmetic Sequences (Intro)?
Make sure you are comfortable with Figurate Numbers, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Arithmetic Sequences (Intro)?
Using n×d instead of (n−1)×d, shifting the answer by one step.
How can I practise Arithmetic 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 Arithmetic Sequences (Intro)?
Move on to Geometric Sequences (Intro) 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.