Sequences
A sequence is an ordered list of numbers called terms that follows a specific pattern or rule. In the sequence 5, 10, 15, 20, the rule is to add 5 each time. The sequence 1, 4, 9, 16 follows the pattern of perfect squares. Identifying the rule lets you predict any term in the sequence. This concept is introduced in Chapter 1 of Saxon Math Course 2 for 7th grade math and develops pattern recognition skills that lead into functions, algebraic expressions, and mathematical modeling.
Key Concepts
Property A sequence is an ordered list of terms that follows a certain pattern or rule.
Examples In the sequence $5, 10, 15, 20, ...$ the rule is to add 5 to the previous term to find the next. The sequence $1, 4, 9, 16, ...$ is a list of perfect squares, following the rule $k = n \cdot n$. The next term is $5 \cdot 5 = 25$. Using the formula $k = 2n$, the first four terms are $2, 4, 6, 8$ (by substituting $n=1, 2, 3, 4$).
Explanation A sequence is like a secret code where numbers follow a hidden rule. Your mission, should you choose to accept it, is to become a pattern detective! By figuring out the rule—whether it's adding, multiplying, or something trickier—you can predict all the future numbers in the line and look like a math magician.
Common Questions
What is a sequence in math?
A sequence is an ordered list of numbers that follows a pattern or rule. Each number in the list is called a term. For example, 5, 10, 15, 20 is a sequence where the rule is adding 5. Sequences can be finite or infinite.
How do you find the rule of a sequence?
Look at the differences between consecutive terms. If the difference is constant, the rule is to add that number. For 5, 10, 15, 20, the difference is always 5, so the rule is add 5. For non-constant differences, look for multiplication patterns or squares.
What is the difference between arithmetic and geometric sequences?
An arithmetic sequence adds the same number each time (like 3, 7, 11, 15 with common difference 4). A geometric sequence multiplies by the same number each time (like 2, 6, 18, 54 with common ratio 3).
How do you find the next term in a sequence?
Apply the identified rule to the last known term. In the sequence 1, 4, 9, 16, the terms are perfect squares (1 squared, 2 squared, 3 squared, 4 squared), so the next term is 5 squared = 25.
What are perfect square sequences?
A perfect square sequence lists the squares of consecutive whole numbers: 1, 4, 9, 16, 25, 36, and so on. The differences between terms increase by 2 each time (3, 5, 7, 9...), which is a useful pattern for identification.
When do students learn about sequences?
Sequences are introduced in 7th grade math as part of pattern recognition. Saxon Math Course 2 covers them in Chapter 1, setting the stage for arithmetic sequences, functions, and algebraic thinking in later chapters.