Patterns and Rules
Patterns in number sequences follow rules that can be described, extended, and used to predict future terms.
What You Need to Know
Key Concept Diagram
A rule describes how each term in a sequence is related to the one before it (e.g. add 5 each time)
Growing patterns increase or decrease by the same amount (arithmetic) or the same ratio (geometric)
A table of values shows the relationship between the position (term number) and the term value
Rules can be written algebraically: if each term adds 3, the nth term is 3n + starting value
Key Vocabulary
Sequence
An ordered list of numbers that follows a rule
Term
Each individual number in a sequence
Rule
A description of how to find the next term or any term in a sequence
Arithmetic sequence
A sequence where the same number is added or subtracted each time (constant difference)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the next term in the sequence: 3, 7, 11, 15, ___?
Question 2
A pattern starts at 2 and multiplies by 3 each time. What is the 4th term?
Question 3
The rule for a sequence is "multiply by 2 then subtract 1". If the 1st term is 3, what is the 3rd term?
Key Concepts Summary
- ●A rule describes how each term in a sequence is related to the one before it (e.g. add 5 each time)
- ●Growing patterns increase or decrease by the same amount (arithmetic) or the same ratio (geometric)
- ●A table of values shows the relationship between the position (term number) and the term value
- ●Rules can be written algebraically: if each term adds 3, the nth term is 3n + starting value