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Sequences and Functions | Year 7 Mathematics (Cambridge) PDF Download
Recognizing Sequences
Sequences are ordered lists of numbers or objects that follow a specific pattern or rule. In mathematics, recognizing sequences helps us understand how numbers relate to each other and predict future terms.
Arithmetic Sequences
- In an arithmetic sequence, each term increases or decreases by a constant difference. For example: 2, 5, 8, 11, 14...
- Example: Identify the common difference in the sequence 3, 7, 11, 15...
Geometric Sequences
- Geometric sequences have a constant ratio between consecutive terms. For example: 2, 6, 18, 54, 162...
- Example: Find the common ratio in the sequence 3, 9, 27, 81...
Identifying Patterns
- Look for recurring patterns or rules that govern how each term is derived from the previous one.
Question for Sequences and Functions
Try yourself:
What is the common difference in the arithmetic sequence: 12, 17, 22, 27...?View Solution
Using Functions
Functions in mathematics describe relationships between inputs (domain) and outputs (range). They can be expressed in various forms, such as equations, tables, or graphs.
Function Notation
- Functions are often denoted as f(x), where x represents the input value.
- Example: Given f(x) = 3x + 2, find f(4).
Function Tables
- Tables organize inputs and corresponding outputs for a function.
- Example: Complete the table for the function g(x) = 2x − 1.
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Graphical Representation
Graphs visually represent functions, showing how inputs and outputs relate.
Example: Plot the graph of h(x) = x2 for −3 ≤ x ≤ 3.
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Summary
Understanding sequences and functions helps in analyzing patterns, predicting future terms in a sequence, and interpreting relationships between variables in functions. Practice identifying different types of sequences and representing functions in various forms enhances mathematical skills and problem-solving abilities.
The document Sequences and Functions | Year 7 Mathematics (Cambridge) is a part of the Year 7 Course Year 7 Mathematics (Cambridge).
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FAQs on Sequences and Functions - Year 7 Mathematics (Cambridge)
| 1. What are some common types of sequences? |  |
| 2. How can functions be used to represent sequences? | |
Ans. Functions can be used to represent sequences by defining a rule or pattern that generates each term in the sequence based on its position.
| 3. How do you determine the next term in a sequence? | |
Ans. To determine the next term in a sequence, you can analyze the pattern or rule that governs the sequence and apply it to find the value of the term at the next position.
| 4. What is the difference between a recursive formula and an explicit formula for a sequence? | |
Ans. A recursive formula defines each term in a sequence based on one or more previous terms, while an explicit formula directly calculates the value of any term based on its position in the sequence.
| 5. Can sequences and functions be used in real-world applications? | |
Ans. Yes, sequences and functions are commonly used in real-world applications such as modeling population growth, predicting future values based on past data, and analyzing patterns in various fields.
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About this Document
Apr 18, 2025
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Document Description: Sequences and Functions for Year 7 2025 is part of Year 7 Mathematics (Cambridge) preparation.
The notes and questions for Sequences and Functions have been prepared according to the Year 7 exam syllabus. Information about Sequences and Functions covers topics
like Recognizing Sequences, Using Functions and Sequences and Functions Example, for Year 7 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Sequences and Functions.
Introduction of Sequences and Functions in English is available as part of our Year 7 Mathematics (Cambridge)
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