Arithmetic Sequence
Arithmetic Sequence is a Grade 8 algebra topic in Saxon Math Course 3, Chapter 7, where students learn that an arithmetic sequence has a constant difference between consecutive terms and can be described by a general term formula. Students identify the common difference, write formulas, and find any term in the sequence, building foundational skills for linear functions and algebra.
Key Concepts
Property An arithmetic sequence has a constant difference between terms. To find it, subtract any term from the one that follows it: $6 3=3$, $9 6=3$.
Examples In the sequence $5, 10, 15, 20, \dots$, the constant difference is $10 5=5$. For the sequence $100, 90, 80, \dots$, the constant difference is $ 10$. The next two terms are $70$ and $60$. The graph of the sequence $2, 4, 6, \dots$ includes the points $(1, 2), (2, 4), (3, 6)$, which form a straight line.
Explanation Think of an arithmetic sequence like climbing a staircase where every step is the same height! You just add the same number, the 'constant difference,' over and over to get the next term. Because the change is steady, if you graph the sequence, the points line up perfectly straight, making it super easy to predict what’s next.
Common Questions
What is an arithmetic sequence?
An arithmetic sequence is a list of numbers where consecutive terms differ by the same constant value called the common difference. For example, 3, 7, 11, 15 is arithmetic with a common difference of 4.
How do you find the common difference in an arithmetic sequence?
Subtract any term from the next term. If the result is the same for all consecutive pairs, that value is the common difference.
What is the formula for the nth term of an arithmetic sequence?
The formula is a_n = a_1 + (n-1) times d, where a_1 is the first term, d is the common difference, and n is the term position.
How is an arithmetic sequence related to linear functions?
An arithmetic sequence grows at a constant rate (the common difference), just like a linear function has a constant slope. Graphing the terms of an arithmetic sequence produces points on a straight line.
Where are arithmetic sequences taught in Grade 8?
Arithmetic sequences are covered in Saxon Math Course 3, Chapter 7: Algebra.