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29 lines
1.1 KiB
Markdown
29 lines
1.1 KiB
Markdown
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# Unit 2: Sequences, Series, and Finicial Applications
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## Terms
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**sequence**: is an ordered set of numbres.
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**Arithmetic Sequences**: is a sequence where the difference between each term is constant, and the constant is known as the `common difference`.
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**Geometric Sequences**: is a sequence in which the ratio between each term is constant, and the constant is known as the `common ratio`.
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**Note:** Not all sequences are arithmetic and geometric!
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**finite series**: finite series have a **finite** number of terms.
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- eg. $`1 + 2 + 3 + \cdots + 10`$.
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**infinite series**: infinite series have **infinite** number of terms.
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- eg. $`1 + 2 + 3 + \cdots`$
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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.
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## Recursion Formula
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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.
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1. Base term(s)
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2. A formula to calculate each successive term.
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eg. $`t_1 = 1, t_n = t_{n-1} + 1 \text{ for } n \ge 1`$
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