What's the difference?
A **sequence** is an ordered list of numbers, like $\{2, 4, 6, 8, \dots\}$. Each number in the sequence is called a **term**. Sequences can be either **finite** (ending) or **infinite** (continuing forever).
A **series** is the sum of the terms of a sequence, like $2 + 4 + 6 + 8 + \dots$. It represents the total value of the numbers in the list.
The two main types you'll study are:
- **Arithmetic**: Each term is found by adding a constant number (the **common difference**, $d$) to the previous term.
- **Geometric**: Each term is found by multiplying a constant number (the **common ratio**, $r$) to the previous term.
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Video: Formulas & Patterns!
Watch this video to understand the patterns and formulas for arithmetic and geometric sequences & series. 🔢
Practice Problems
Solve these problems about sequences and series!
1) Is $\{10, 8, 6, 4, \dots\}$ arithmetic or geometric?
2) What is the common ratio of $\{3, 9, 27, \dots\}$?
3) What is the 5th term of the arithmetic sequence with $a_1=5$ and $d=2$?
4) What is the sum of the series $1+2+3+4+5$?
⚡ Sequences & Series Speed Quiz
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