11-4 Arithmetic Series - Poudre School District
11 4 Arithmetic Series April 27, 2009 11 4 Arithmetic Series Objectives: Write and evaluate arithmetic series. Use summation notation. Apr 21 4:15 PM 1
11 4 Arithmetic Series April 27, 2009 Find each sum. 1. 2 3.5 5 6.5 8 2. 17 ( 13) ( 9) ( 5) ( 1) 3 Write an explicit formula for each sequence. 3. 4, 6, 7, 10, 12,. 4. 1, 4, 7, 10, 13, 16,. 5. 17, 23, 29, 35,. 6. 10, 1, 8, 17,. Apr 21 4:16 PM 2
11 4 Arithmetic Series April 27, 2009 Apr 21 4:17 PM 3
11 4 Arithmetic Series April 27, 2009 Series: The expression for the sum of the terms of a sequence. Finite Sequence 6, 9, 12, 15, 18 Finite Series 6 9 12 15 18 Infinite Sequence 3, 7, 11, 15,. Infinite Series 3 7 11 15 . Apr 21 4:17 PM 4
11 4 Arithmetic Series April 27, 2009 Example #1: Writing and Evaluating a Series Use the finite sequence 2, 11, 20, 29, 38, 47. a. Write the related series. 2 11 20 29 38 47 b. Evaluate the series. 2 11 20 29 38 47 147 Apr 21 4:17 PM 5
11 4 Arithmetic Series April 27, 2009 Arithmetic Series: A series whose terms form an arithmetic sequence. Apr 21 4:18 PM 6
11 4 Arithmetic Series April 27, 2009 Apr 21 4:18 PM 7
11 4 Arithmetic Series April 27, 2009 Apr 21 4:19 PM 8
11 4 Arithmetic Series April 27, 2009 You can use the summation symbol Ʃ to write a series. Then you can use limits to indicate how many terms you are adding. Ʃ is the Greek capital letter sigma, the equivalent of the English letter S (for summation). Apr 21 4:19 PM 9
11 4 Arithmetic Series April 27, 2009 Example #3: Writing a Series in Summation Notation Use summation notation to write the series 3 6 9 . for 33 terms. Step 1: Write the explicit formula. an a1 d(n 1) an 3 3(n 1) an 3n Step 2: Write in summation notation including the limits of n. 33 3n n 1 Apr 21 4:20 PM 10
11 4 Arithmetic Series April 27, 2009 Example #4: Writing a Series in Summation Notation Use summation notation to write the series 3 8 13 18. for n 9. Step 1: Write the explicit formula. an a1 d(n 1) an 3 5(n 1) an 5n 2 Step 2: Write in summation notation including the limits of n. 9 (5n 2) n 1 Apr 21 4:20 PM 11
11 4 Arithmetic Series April 27, 2009 To expand a series from summation notation, you can substitute each value of n into the explicit formula and add the results. Apr 21 4:20 PM 12
11 4 Arithmetic Series April 27, 2009 Example #5: Finding the Sum of a Series 3 Use the series (5n 1). n 1 a. Find the number of terms in the series. 3 terms n 1, 2, 3 b. Find the first and last terms of the series. a1 5(1) 1 6 an 5(3) 1 16 c. Evaluate the series. 3 (5n 1) (5(1) 1) (5(2) 1) (5(3) 1) n 1 6 11 16 33 Apr 21 4:20 PM 13
11 4 Arithmetic Series April 27, 2009 Example #6: For each sum, find the number of terms, the first term, and the last term. Then evaluate each series. n Sn 4 10 a. (n 3) n 1 b. 1 2 ( n 1) n 1 2 (a1 an) 5 c. n2 n 2 Apr 21 4:21 PM 14
11 4 Arithmetic Series April 27, 2009 Homework: page 622 (2 32 even, 37, 40) Apr 21 4:23 PM 15
Arithmetic Series: A series whose terms form an arithmetic sequence. 11 4 Arithmetic Series 7 April 27, 2009 Apr 21 4:18 PM. 11 4 Arithmetic Series 8 April 27, 2009 Apr 21 4:19 PM. 11 4 Arithmetic Series . Homework: page 622 (2 32 even, 37, 40) Title: 11-4 Arithmetic Series Subject: SMART Board Interactive Whiteboard Notes
3.2 Arithmetic series: the sum of an arithmetic sequence Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life. 7C 7D Arithmetic Sequence Arithmetic Series 6C 6D Arithmetic sequences Arithmetic series 3.1 3.2 Arithmetic sequence Arithmetic s
arithmetic sequence finds the nth term of an arithmetic sequence lists down the first few terms of an arithmetic sequence given the general term and vice-versa solves word problems involving arithmetic mean applies the concepts of mean and the nth term of an arithmetic sequence
9 4 Arithmetic Series An arithmetic series is an indicated sum of the terms of an arithmetic sequence. A finite series has a first term and a last term. An infinite series continues without end. To find the sum of a finite arithmetic series use . . . where n is the number of terms. May 19 9:07 PM
arithmetic sequence are called arithmetic means. In the sequence below, 38 and 49 are the arithmetic means between 27 and 60. 5, 16, 27, 38 , 49 , 60 760 Chapter 12 Sequences and Series The n th term of an arithmetic sequence with first term a 1 and common difference d is given by a n a 1 (n 1) d . The n th Term of an Arithmetic Sequence .
2.2 Affine Arithmetic Themodeling tool in thispaper is a ne arithmetic, which is an e cient and recent variant of range arithmetic. In this section, we begin with introducing its predecessor, inter-val arithmetic, and then emphasize the advantage of a ne arithmetic. Interval arithmetic (IA), also known as interval analysis,
Cache la Poudre River Natural Areas Management Plan Update 2011 Ch. 1 Purpose, Scope and Process 1 CHAPTER 1 A. Vision for the Poudre River Natural Areas
The Cache la Poudre River: From Snow to Flow The Cache la Poudre River is located in northern Colorado. It spans nearly 130 miles in length and drops over 6,100 feet (1860 meters) in elevation. The river is a popular destination for rafting and fishi
It is not strictly a storage tank and it is not a pressure vessel. API does not have a standard relating to venting capacities for low-pressure process vessels. It is recommended that engineering calculations be performed based on process and atmospheric conditions in order to determine the proper sizing of relief devices for these type vessels. However, it has been noted that may people do .
