Grade 11 · Algebra & Functions
Sequences and Series
Learn to identify rules that generate ordered patterns through clear explanations, worked examples, an interactive model, and guided practice.
Lesson coverage
Learn the whole topic, not just one problem type.
This lesson and its practice bank deliberately rotate across these core facets so students build a connected understanding of the subject.
Identify how terms change.
Use a rule to find later terms.
Connect term number to term value.
Describe how each term comes from previous terms.
Model repeated change with sequences.
Build the idea
Sequences and Series is part of the extend functions and algebra to polynomial, rational, radical, exponential, logarithmic, complex, and trigonometric relationships. Start by identifying what each quantity, symbol, diagram, or graph represents before calculating.
Recognize patterns
Identify how terms change. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Generate terms
Use a rule to find later terms. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Explicit rules
Connect term number to term value. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Recursive rules
Describe how each term comes from previous terms. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Applications
Model repeated change with sequences. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Use a reliable strategy
Translate the information into symbols, apply one valid transformation at a time, and check the result in the original relationship.
Check and explain
A correct answer is only part of mathematical understanding. Check units, signs, scale, and whether the result makes sense. Then explain the relationship in words so you can recognize the same structure when the numbers or context change.
Key terms
Words to know
- Sequences and Series
- The central skill or relationship explored in this lesson.
- Sequence
- An ordered list generated by a rule.
- Term
- One entry in a sequence.
- Common difference
- The constant change in an arithmetic sequence.
Interactive math lab
Change it. See it. Understand it.
Adjust the values and watch the relationship respond.
| Input | 6 |
|---|---|
| Offset | 3 |
| Output | 15 |
Worked examples
See the idea in action.
Add the common difference 3 again.
An explicit arithmetic rule gives any term directly from the first term and common difference.
Guided practice
20 questions drawn from a 150-question lesson bank.
Each practice session mixes the major skills in this lesson so you practice the whole topic, not just one repeated problem type.
What is the common difference in 2, 4, 6, ...?
Curriculum reference
Built as a continuous K–12 progression.
The sequence follows widely used K–12 mathematics progressions and references the Common Core mathematics framework. Explanations, examples, interactive models, and practice questions are original FreeLearnHub material.