9 4 Arithmetic Series - PC\ MAC
Alg2Hon 9 4 and 9 5 Notes and answers.notebookMay 20, 20139 4 Arithmetic SeriesAn arithmetic series is an indicated sum of theterms 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.Oct 27 9:07 AMExample 1. (p. 588) Got It? 1aWhat is the sum of the finite arithmetic series4 9 14 19 24 . . . 99?How to find n (the number of terms)1. Find common difference (d)2. Subtract last term first term3. Divide by d4. Add 1 (to count first term)May 19 9:07 PM1
Alg2Hon 9 4 and 9 5 Notes and answers.notebookMay 20, 2013Example 2What is the sum of the finite arithmetic series14 17 20 23 . . . 116?You can also use the formula for the nth termin an arithmetic sequence to find n.an a1 (n 1)dMay 19 9:10 PMan a1 (n 1)dExample 3 (p. 588) Got It? 2.A company pays a 5,000 bonus if a new salesperson makes 10 sales inthe first week and then improves by one sale per week each weekthereafter. One salesperson qualified for this bonus with the minimumnumber of sales. How many sales did the salesperson make in week50? In all 50 weeks?May 19 9:16 PM2
Alg2Hon 9 4 and 9 5 Notes and answers.notebookMay 20, 2013Sigma Notation(Denotes the sum of a series)Oct 27 9:07 AM(p. 589)May 19 9:22 PM3
Alg2Hon 9 4 and 9 5 Notes and answers.notebookExample 4 (p. 589) Got It? 3What is summation notation for the series?a. 5 2 9 16 . . . 261 268May 20, 2013an a1 (n 1)db. 500 490 480 . . . 20 10May 19 9:40 PMExample 5Evaluatea.b.Oct 27 9:07 AM4
Alg2Hon 9 4 and 9 5 Notes and answers.notebookMay 20, 2013(p. 589)If the explicit formula is not linear, then you can evaluate thesum by adding the terms.Example 6 (p. 590) Got It? 4b 4cMay 19 9:50 PM9 5 Geometric SeriesA geometric series is an indicated sum of the terms ofa geometric sequence.To find the sum of a finite geometric series use . . .Oct 27 9:07 AM5
Alg2Hon 9 4 and 9 5 Notes and answers.notebookMay 20, 2013Example 1Evaluate the sum of the finite geometric seriesa. (p. 599) 8. 1 2 4 8 . . . 128Nth term in a Geometric Sequencean a1rn 1b. (p. 599) 10. 3 6 12 24 48 . . . 768May 20 10:18 AMExample 2 (p. 596) Got It? 1bWhat is the sum of the finite geometric series?May 20 10:22 AM6
Alg2Hon 9 4 and 9 5 Notes and answers.notebookMay 20, 2013Example 3 (p. 597) Got It? 2May 20 10:24 AMInfinite Geometric Series An infinite geometric series is the sum of a geometricseries with r 1 (that is, 1 r 1 ) An infinite geometric series for which r 1( that is, r 1 or r 1), does not have a sum (thesum does not exist)Oct 27 9:07 AM7
Alg2Hon 9 4 and 9 5 Notes and answers.notebookMay 20, 2013Find the sum of the infinitie geometric series, if it exists.1. a1 4, r 5/72. 1 2/3 4/9 3.4. The sum of an infinite geometric series is 81, and its commonration is 2/3. Find the first three terms of the series.Oct 27 9:07 AMRepeating DecimalsWrite 0.16666666 as a fraction.Oct 27 9:07 AM8
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
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 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
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
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,
Arithmetic & Geometric Sequences Worksheet Level 2: Goals: Identify Arithmetic and Geometric Sequences Find the next term in an arithmetic sequence Find the next term in a geometric sequence Practice #1 Does this pattern represent an arithmetic or geometric sequence? Explain. Find how many dots would be in the next figure?
Arithmetic Sequence Formula Examples Partial Sums Formula Examples Homework General Way to Write an Arithmetic Sequence Way to Write a Formula for an Arithmetic Sequence: Given that a 1;a 2;a 3;::: is an arithmetic sequence with common di erence d, We can rewrite the sequence as a n a 1 (n 1)d where the index starts at n 1. Here a
Pile designers therefore looked at calculation based on theoretical soil mechanics. 16 Geotechnical Design to EC7 13 January 2017 Layer 1 Layer 2 Layer 3 L 1 L 2 L 3 Q s1 Q s2 Q s3 Q b Ultimate pile resistance Q u Q s Q b Traditional Pile Design to BS 8004. 17 Geotechnical Design to EC7 13 January 2017 Traditional Pile Design to BS 8004 The usual approach is to divide the ground into .
