6 Questions
What is a sequence of numbers that follows a specific rule or formula?
Number pattern
In an arithmetic sequence, each term is obtained by?
Adding a fixed constant to the previous term
What is the sequence of numbers in which each term is the sum of the two preceding terms?
Fibonacci sequence
What is a single number in a sequence?
Term
What is the term that comes after a given term in a sequence?
Next term
In what field is the pattern of stock prices or economic trends an application of number patterns?
Finance
Study Notes
Introduction to Number Patterns
- A number pattern is a sequence of numbers that follow a specific rule or formula.
- Number patterns can be found in nature, art, and mathematics.
Types of Number Patterns
-
Arithmetic Sequences: A sequence of numbers in which each term is obtained by adding a fixed constant to the previous term.
- Example: 2, 5, 8, 11, ...
-
Geometric Sequences: A sequence of numbers in which each term is obtained by multiplying the previous term by a fixed constant.
- Example: 2, 6, 18, 34, ...
-
Fibonacci Sequence: A sequence of numbers in which each term is the sum of the two preceding terms.
- Example: 0, 1, 1, 2, 3, 5, 8, ...
Characteristics of Number Patterns
- Rule: A formula or equation that defines the pattern.
- Term: A single number in the sequence.
- Next Term: The term that comes after a given term in the sequence.
- Previous Term: The term that comes before a given term in the sequence.
Creating Number Patterns
- Start with a Rule: Identify the rule or formula that defines the pattern.
- Use the Rule to Generate Terms: Apply the rule to generate each term in the sequence.
- Recognize Patterns: Look for relationships between terms to identify the pattern.
Real-World Applications of Number Patterns
- Science: Patterns in nature, such as the arrangement of leaves on a stem or the branching of trees.
- Finance: Patterns in stock prices or economic trends.
- Computer Science: Patterns in algorithms and data structures.
Introduction to Number Patterns
- A number pattern is a sequence of numbers that follow a specific rule or formula, and they can be found in nature, art, and mathematics.
Types of Number Patterns
- Arithmetic Sequences: Each term is obtained by adding a fixed constant to the previous term, e.g., 2, 5, 8, 11,....
- Geometric Sequences: Each term is obtained by multiplying the previous term by a fixed constant, e.g., 2, 6, 18, 34,....
- Fibonacci Sequence: Each term is the sum of the two preceding terms, e.g., 0, 1, 1, 2, 3, 5, 8,....
Characteristics of Number Patterns
- Rule: A formula or equation that defines the pattern.
- Term: A single number in the sequence.
- Next Term: The term that comes after a given term in the sequence.
- Previous Term: The term that comes before a given term in the sequence.
Creating Number Patterns
- Start with a Rule: Identify the formula or equation that defines the pattern.
- Use the Rule to Generate Terms: Apply the rule to generate each term in the sequence.
- Recognize Patterns: Look for relationships between terms to identify the pattern.
Real-World Applications of Number Patterns
- Science: Patterns in nature, such as the arrangement of leaves on a stem or the branching of trees.
- Finance: Patterns in stock prices or economic trends.
- Computer Science: Patterns in algorithms and data structures.
Learn about number patterns, including arithmetic and geometric sequences, and their applications in nature, art, and mathematics.
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