Number Patterns and Sequences

Study Notes

A number pattern is a sequence of numbers that follow a specific rule or relationship.

Arithmetic Sequence: A sequence of numbers in which each term is obtained by adding a fixed constant to the previous term.
- Example: 2, 5, 8, 11, 14...
- Formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.
Geometric Sequence: A sequence of numbers in which each term is obtained by multiplying the previous term by a fixed constant.
- Example: 2, 6, 18, 34, 50...
- Formula: an = a1 × r^(n-1), where an is the nth term, a1 is the first term, and r is the common ratio.
Quadratic Sequence: A sequence of numbers in which each term is obtained by adding a fixed constant to the square of the previous term.
- Example: 1, 4, 9, 16, 25...
- Formula: an = an-1 + 2n - 1, where an is the nth term.

Look for a consistent difference or ratio between consecutive terms.
Check if the sequence follows a specific formula or relationship.
Use visual representations, such as number lines or graphs, to help identify patterns.

Number patterns are used in finance to calculate interest rates and investment returns.
They are used in science to model population growth and chemical reactions.
They are used in computer programming to write algorithms and solve problems.

Start by identifying the type of sequence (arithmetic, geometric, or quadratic).
Use the formula to find the next term or to identify the pattern.
Practice solving different types of number patterns to improve your skills.

A number pattern is a sequence of numbers that follow a specific rule or relationship.

Arithmetic Sequence: Each term is obtained by adding a fixed constant to the previous term.
- Example: 2, 5, 8, 11, 14...
- Formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.
Geometric Sequence: Each term is obtained by multiplying the previous term by a fixed constant.
- Example: 2, 6, 18, 34, 50...
- Formula: an = a1 × r^(n-1), where an is the nth term, a1 is the first term, and r is the common ratio.
Quadratic Sequence: Each term is obtained by adding a fixed constant to the square of the previous term.
- Example: 1, 4, 9, 16, 25...
- Formula: an = an-1 + 2n - 1, where an is the nth term.

Look for a consistent difference or ratio between consecutive terms.
Check if the sequence follows a specific formula or relationship.
Use visual representations, such as number lines or graphs, to help identify patterns.

Number patterns are used in finance to calculate interest rates and investment returns.
They are used in science to model population growth and chemical reactions.
They are used in computer programming to write algorithms and solve problems.

Identify the type of sequence (arithmetic, geometric, or quadratic) to start solving.
Use the formula to find the next term or to identify the pattern.
Practice solving different types of number patterns to improve skills.