PPT-Sequences and Series Number sequences, terms, the general term, terminology.

Formulas booklet page 3 In maths we call a list of numbers in order a sequence Each number in a sequence is called a term 4 8 12 16 20 24 28 32 1 st term 6 th term. By: Matt Connor. Fall 2013. Pure Math. Analysis. Calculus and Real Analysis . Sequences. Sequence- A list of numbers or objects in a specific order. 1,3,5,7,9,...... Finite Sequence- contains a finite number of terms. An introduction…………. Arithmetic Sequences. ADD. To get next term. Geometric Sequences. MULTIPLY. To get next term. Arithmetic Series. Sum of Terms. Geometric Series. Sum of Terms. Find the next four terms of –9, -2, 5, …. Informally, a sequence is a set of elements written in a row.. This concept is represented in CS using one-dimensional arrays. The goal of mathematics in general is to identify, prove, and utilize patterns. 4. Sequences and Mathematical Induction. 4.1. Sequences. Sequences. The main mathematical structure used to study repeated processes is the sequence.. The main mathematical tool used to verify conjectures about patterns governing the arrangement of terms in sequences is mathematical induction.. Section 2.4. Section Summary. Sequences.. Examples: Geometric Progression, Arithmetic Progression. Recurrence Relations. Example: Fibonacci Sequence. Summations. Introduction. Sequences are ordered lists of elements. . Section 8.3 beginning on page 426. Geometric Sequences. In a . geometric sequence. , the ratio of any term to the previous term is constant. This constant ratio is called the . common ratio. . and is denoted by . Sequences. Dr J Frost (jfrost@tiffin.kingston.sch.uk. ). www.drfrostmaths.com. . Last modified: . 6. th. November 2015. Objectives: . Understand term-to-term vs position-to-term rules.. . Be able to generate terms of a sequence given a formula. Find the formula for a linear sequence.. Chapter 12. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Dr J Frost (jfrost@tiffin.kingston.sch.uk). www.drfrostmaths.com. . Last modified: . 19. th. . October 2015. Teacher Guidance. Possible lesson structure:. Lesson 1. : Linear Sequences Recap and generating sequences . Goals and Objectives. Students will be able to understand how the common difference leads to the next term of an arithmetic sequence, the explicit form for an Arithmetic sequence, and how to use the explicit formula to find missing data.. 1, 1, 2, 3, 5, 8, 13, ….. 1, 4, 9, 16, 25, 36, …. 6, 10, 14, 18, 22, …. 7, 14, 28, 56, ….. . , , , …... Unit 3 Part C:. Arithmetic and Geometric Sequences. F.IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. . Consider the following sequence . , . , . , . ,…. Each term of this sequence is of the form .  . What happens to these terms as n gets very large? . In general, the . , for all positive r .  . Many sequences have limiting factors. Difference. Equations. (5.1) Sequences. (5.2) Limit of a Sequence . (5.3) Discrete Difference Equations. (5.4) Geometric & Arithmetic Sequences. (5.5) Linear Difference Equation with Constant Coefficients (scanned notes). A sequence or progression is an ordered set of numbers which can be generated from a rule.. General sequence terms as denoted as follows. a. 1 . – first term. . , a. 2. – second term, …, a. n.