PPT-9.2 – Arithmetic Sequences and Series

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 . CSE235 Introduction Sequences Summations Series Sequences Denition AsequenceisafunctionfromasubsetofintegerstoasetS.Weusethenotation(s):fangfang1nfang1n=0fang1n=0Eachaniscalledthen-thtermofthesequenc 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. CS1313 Spring 2016. 1. Arithmetic Expressions Lesson #2 Outline. Arithmetic Expressions Lesson #2 Outline. Named Constant & Variable Operands #1. Named Constant & Variable Operands #2. Named Constant & Variable Operands #2. Section 10.1. Sequences. Section 10.2. Infinite Series. Section 10.3. The Integral Test. 10.4. Comparison Tests. Section 10.5. Absolute Convergence; The . Ratio and Root Tests. Section 10.6. Alternating . a. 1 . = 5, d = 12, n = 28. a. 28. = 329. 1. Find the indicated term of the arithmetic sequence.. a. 1 . = 5, d = 12, n = 28. 2. Find the 23. rd. term of the following sequence.. 6, 18, 30, 42, …. Arithmetic Sequences. An arithmetic sequence is a sequence in which each term after the first differs from the preceding term by a constant amount.. The difference between consecutive terms is called the . 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.. 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.. 2, 4, 6, 8, . …. The . first term in a sequence is denoted as . a. 1. , . the second term is . a. 2. , . and so on up to the nth term . a. n. .. Each number in the list called a . term. .. a. 1. , a. Lesson 3.13 Applications of Arithmetic Sequences Concept: Arithmetic Sequences EQ: How do we use arithmetic sequences to solve real world problems? F.LE.2 Vocabulary: Arithmetic sequence, Common difference 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. 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. 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. & Series. Story Time…. When another famous mathematician was in first grade, his teacher asked the class to add up the numbers one through a hundred (1+2+3 etc., all the way up to 100). . Write out the teacher’s request in summation notation, then find the answer (no calculators!) Try to figure out an efficient way!.