Sequences - IELTS Academic Writing IELTS Study Notes
Overview
Imagine you're building with LEGOs, and each new piece you add follows a special rule. Or think about the way your height changes every year – it's not random, right? That's what sequences are all about! In maths, a sequence is just a list of numbers that follow a pattern, like a secret code. Understanding sequences helps us predict what comes next, whether it's how much money you'll save each month or how a population might grow. It's like being a detective for numbers! Even though you might not see 'sequences' directly in your IELTS Academic Writing, the skills you learn from understanding patterns and logical progression are super important for structuring your essays and making your arguments flow smoothly. It helps you think in an organised way, which is key to getting a good score!
What Is This? (The Simple Version)
Imagine you're lining up your favourite toys, one after another. If you always put a red car, then a blue car, then a green car, and then repeat, you've made a sequence! In maths, a sequence is simply a list of numbers that follow a specific rule or pattern.
Think of it like a treasure hunt where each clue (number) tells you how to find the next one. Each number in the list is called a term. So, in the sequence 2, 4, 6, 8..., the first term is 2, the second term is 4, and so on. The 'rule' here is to add 2 to get the next number. It's like counting by twos forever!
Real-World Example
Let's say you're saving money for a new video game. Your parents agree to give you £5 on the first day, £10 on the second day, £15 on the third day, and so on. This is a sequence!
- Day 1: £5 (This is your first term)
- Day 2: £10 (Your second term)
- Day 3: £15 (Your third term)
Can you guess how much you'd get on Day 4? If you said £20, you got it! The rule (or common difference) here is that you add £5 each day. This type of sequence, where you add or subtract the same amount each time, is called an arithmetic sequence. It's like climbing stairs where each step is the same height.
How It Works (Step by Step)
Let's break down how to understand and find the next numbers in a sequence: 1. **Look for the pattern:** Start by comparing the first two numbers. What did you do to get from the first to the second? (Did you add, subtract, multiply, or divide?) 2. **Test the pattern:** Apply that same action to ...
Unlock 3 More Sections
Sign up free to access the complete notes, key concepts, and exam tips for this topic.
No credit card required · Free forever
Key Concepts
- Sequence: A list of numbers that follow a specific rule or pattern.
- Term: Each individual number in a sequence.
- Pattern/Rule: The consistent way numbers change from one term to the next in a sequence.
- Arithmetic Sequence: A sequence where you add or subtract the same number to get the next term.
- +4 more (sign up to view)
Exam Tips
- →For IELTS Academic Writing, understanding sequences helps you structure your arguments logically, ensuring a smooth flow from one point to the next.
- →Practice identifying patterns in data presented in graphs or tables; this skill is like finding the rule in a sequence.
- +2 more tips (sign up)
More Mathematics Notes