From 5ee3f10c92e70d9066d9ab599167b5621a41aa94 Mon Sep 17 00:00:00 2001 From: James Su Date: Fri, 6 Mar 2020 16:04:39 +0000 Subject: [PATCH] Add new file --- ...ces, Series, and Financial Applications.md | 29 +++++++++++++++++++ 1 file changed, 29 insertions(+) create mode 100644 Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md diff --git a/Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md b/Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md new file mode 100644 index 0000000..ff98b97 --- /dev/null +++ b/Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md @@ -0,0 +1,29 @@ +# 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. $`t_1 = 1, t_n = t_{n-1} + 1 \text{ for } n \ge 1`$ \ No newline at end of file