Sequences & Series - Complete Interactive Lesson
Part 1: Arithmetic Sequences
๐ Sequences & Series โ Arithmetic Sequences
Part 1 of 7
What Is a Sequence?
A sequence is an ordered list of numbers following a pattern. Each number is called a term.
Arithmetic Sequences
An arithmetic sequence has a constant difference between consecutive terms:
where is the common difference.
Examples
- โ
- โ
๐ Finding Terms and Sums
The th Term Formula
๐งฉ Applications
Finding Unknown Terms
If and :
Arithmetic Sequences Quiz ๐ฏ
Arithmetic Sequence Practice ๐งฎ
1) . Find :
Arithmetic Sequences Properties ๐ฝ
Exit Quiz โ
Part 2: Geometric Sequences
๐ Geometric Sequences
Part 2 of 7
Definition
A geometric sequence has a constant ratio between consecutive terms:
Part 3: Series & Partial Sums
โพ๏ธ Infinite Geometric Series
Part 3 of 7
When Does an Infinite Sum Converge?
For a geometric series with , the partial sums approach a finite limit:
Part 4: Sigma Notation
๐ข Sigma Notation & Series
Part 4 of 7
Sigma (Summation) Notation
Part 5: Infinite Geometric Series
๐ Recursive Sequences & Special Sequences
Part 5 of 7
Recursive vs. Explicit Formulas
| Type | Definition | Example |
|---|---|---|
| Explicit | as a function of |
Part 6: Problem-Solving Workshop
๐งฎ Binomial Theorem
Part 6 of 7
Pascal's Triangle
Part 7: Review & Applications
๐ฏ Sequences & Series โ Full Synthesis
Part 7 of 7
Master Summary
| Type | th Term | Sum Formula | Convergence |
|---|---|---|---|
| Arithmetic |