Sequence
A sequence in Grade 7 math is an ordered list of numbers arranged according to a specific rule. In Saxon Math, Course 2, students identify rules for sequences by examining how consecutive terms relate. For example, in 1, 3, 6, 10, ..., each term increases by one more than the last. Recognizing sequence patterns — whether arithmetic (add/subtract a constant) or geometric (multiply/divide by a constant) — develops algebraic thinking and function reasoning that students use throughout middle and high school math.
Key Concepts
Property A sequence is a list of terms arranged according to a certain rule.
Examples The sequence $1, 3, 6, 10, ...$ increases by one more each time. The next term is $10 + 5 = 15$. In the sequence $40, 35, 30, 25, ...$, the rule is to subtract 5. The next term is $25 5 = 20$. The sequence $2, 6, 18, 54, ...$ follows the rule of multiplying by 3. The next term is $54 \times 3 = 162$.
Explanation Imagine you are a detective cracking a code! A sequence is just a line of numbers following a secret rule. Your job is to figure out that pattern. Is it adding 2 each time, or maybe something trickier?
Common Questions
What is a sequence in Grade 7 math?
A sequence is an ordered list of terms that follow a specific rule. Each term is related to the previous one by a consistent pattern.
How do you find the rule of a sequence?
Look at the difference or ratio between consecutive terms. If the difference is constant (like always adding 5), it is arithmetic. If the ratio is constant (like always multiplying by 2), it is geometric.
How do you find the next term in a sequence?
Apply the identified rule to the last term. For example, in 40, 35, 30, 25, ..., the rule is subtract 5, so the next term is 20.
What is the difference between an arithmetic and geometric sequence?
In an arithmetic sequence, the same number is added or subtracted each time (equal spacing). In a geometric sequence, each term is multiplied by the same factor.
Where are sequences taught in Saxon Math Course 2?
Sequences are introduced in Saxon Math, Course 2, as part of Grade 7 patterns, functions, and algebraic reasoning content.
Can a sequence have a decreasing pattern?
Yes. Sequences can increase or decrease. For example, 40, 35, 30, 25 decreases by subtracting 5 each time.
How do sequences relate to functions in math?
A sequence is a function where the input is the position number (1st, 2nd, 3rd...) and the output is the term value. Recognizing sequence rules is foundational to understanding functions.