mirror of
https://gitlab.com/magicalsoup/Highschool.git
synced 2025-01-24 08:31:45 -05:00
29 lines
1.1 KiB
Markdown
29 lines
1.1 KiB
Markdown
# Unit 2: Sequences, Series, and Finicial Applications
|
|
|
|
|
|
## Terms
|
|
**sequence**: is an ordered set of numbres.
|
|
|
|
**Arithmetic Sequences**: is a sequence where the difference between each term is constant, and the constant is known as the `common difference`.
|
|
|
|
**Geometric Sequences**: is a sequence in which the ratio between each term is constant, and the constant is known as the `common ratio`.
|
|
|
|
**Note:** Not all sequences are arithmetic and geometric!
|
|
|
|
**finite series**: finite series have a **finite** number of terms.
|
|
- eg. $`1 + 2 + 3 + \cdots + 10`$.
|
|
|
|
**infinite series**: infinite series have **infinite** number of terms.
|
|
- eg. $`1 + 2 + 3 + \cdots`$
|
|
|
|
Terms in a sequence are numbered with subscripts: $~t_1, t_2, t_3, \cdots t_n`$ where $`t_n`$is the general or $`n^{th}`$ term.
|
|
|
|
|
|
## Recursion Formula
|
|
|
|
A sequence is defined recursively if you have to calculate a term in a sequence from previous terms. The recursion formula consist of 2 parts.
|
|
|
|
1. Base term(s)
|
|
2. A formula to calculate each successive term.
|
|
|
|
eg. $`t_1 = 1, t_n = t_{n-1} + 1 \text{ for } n \ge 1`$ |