A recursive pattern rule in Grade 6 math describes how a pattern starts and how it continues to generate subsequent terms. This type of rule is based on the relationship between consecutive terms in a sequence. According to the provided reference, a recursive pattern rule "tells you the start number of a pattern and how the pattern continues".
Understanding Recursive Pattern Rules
Here's a breakdown of what constitutes a recursive pattern rule:
- Starting Number: This identifies the first term in the sequence.
- Continuation Rule: This describes how to get from one term to the next. This often involves addition, subtraction, multiplication, or division of a constant value, known as the common difference or common ratio.
Examples of Recursive Pattern Rules
Let's look at some examples to illustrate recursive pattern rules:
Example 1: 5, 8, 11, 14, ...
- Starting Number: 5
- Continuation Rule: Add 3 to the previous term.
- Recursive Rule: Start with 5, and add 3.
- Common Difference: 3
Example 2: 2, 4, 8, 16, ...
- Starting Number: 2
- Continuation Rule: Multiply the previous term by 2.
- Recursive Rule: Start with 2, and multiply by 2.
- Common Ratio: 2
Example 3: 20, 17, 14, 11, ...
- Starting Number: 20
- Continuation Rule: Subtract 3 from the previous term.
- Recursive Rule: Start with 20, and subtract 3.
- Common Difference: -3
Key Components of a Recursive Pattern
A recursive pattern rule identifies:
- The first term in the sequence.
- The operation (addition, subtraction, multiplication, division) to perform on the previous term.
- The value to be used in the operation (common difference or ratio).
How to Define a Recursive Pattern Rule
To define a recursive pattern rule, follow these steps:
- Identify the first term.
- Determine the operation between consecutive terms: Is it addition, subtraction, multiplication, or division?
- Find the common difference or ratio: What value is being added, subtracted, multiplied, or divided to get from one term to the next?
- Write the rule: Start with the first term, and then state the operation and value.
