Number Patterns and Sequences
A sequence is an ordered list of numbers that follow a rule. Identifying and describing patterns helps us predict future terms and understand algebraic relationships.
What You Need to Know
Key Concept Diagram
An arithmetic sequence increases or decreases by a constant amount (the common difference)
A geometric sequence multiplies each term by a constant ratio
The rule for the nth term of an arithmetic sequence is: T(n) = a + (n-1)d, where a is the first term and d is the common difference
Patterns can be represented with tables of values and graphs
Key Vocabulary
Sequence
An ordered list of numbers that follow a rule
Term
Each number in a sequence
Common difference
The constant amount added between successive terms in an arithmetic sequence
nth term rule
A formula that gives the value of any term in a sequence based on its position n
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
What is the 10th term of the sequence with first term 2 and common difference 5?
Question 3
Which sequence is geometric?
Key Concepts Summary
- ●An arithmetic sequence increases or decreases by a constant amount (the common difference)
- ●A geometric sequence multiplies each term by a constant ratio
- ●The rule for the nth term of an arithmetic sequence is: T(n) = a + (n-1)d, where a is the first term and d is the common difference
- ●Patterns can be represented with tables of values and graphs