1 a a a a a Write a formula for a 6 in terms of a 5.

Transcription

1 Sectio 1.1 Arithmetic Sequeces ad Series Basic Terms A sequece is a ordered list of umbers. Each umber i a sequece is called a term. Work Together Usig the sequece give at the right. Fid the sixth term i the sequece, a. Write a formula for a i terms of a 5. Geeralize your formula by writig a formula for a i terms of a -1. Number of the term Term Symbol Term 1 a 1 9 a 1 3 a 3 19 a 5 a 5 9 Note: This geeral formula is called a formula. Def -- the formula defies the term i a by relatig each term to the oe it. Thik ad Discuss Arithmetic Sequece -- Commo Differece -- Are the give sequeces arithmetic? If so idetify the commo differeces. {, 5, 7, 1,...} {8, 5,, 39,...} What is the 15th term i the sequece, a 15, i the d problem? How did you fid it? Explicit Formula -- expresses the term i terms of. Writ a explicit formula for the secod problem above. Check your formula with the aswer came up for the 15th term. How did you fid the formula Geeral Formula for arithmetic Sequeces --- Try It -- Fid the 5th term of {0, 17, 1, 11, 8,...} Arithmetic Mea --- Try it -- Fid the two arithmetic meas betwee - ad 5. Precalculus Chapter 1 Page 1

2 Series -- expressio for the of the terms i a. Fid the sum of this series How did you come up with your aswer? Formula -- Try It -- Fid the sum of the series A school committee has decided sped a large portio of its aual techology budget o ipads. This year, the techology coordiator bought 75 ipads. She plas to buy 5 ew ipads each year after that. Suppose the school committee has decided that each studet should have access to a ipad withi seve years. The schools populatio is 500. Will the techology coordiator meet this goal? Explai. Homework: p. 73 1,,, (18-8)/3, 5, 57, 59-9 all (excludig 3,7,8) Precalculus Chapter 1 Page

3 Sectio 1. Geometric Sequeces ad Series Work Together Make a large right isosceles triagle. Cut the triagle ito two equal isosceles triagles. Repeat the process with the two triagles formed. Cotiue this process four times. Is the sequece of triagles arithmetic? Fid the sixth term, a, i the sequece. Write a recursive formula for a i the terms of a -1. Graph the sequece of the triagles o a grid usig the as x ad a as y. Ay thig familiar about this graph? Graph this arithmetic sequece {1,3,5,7,...}. How are the two graphs differet? Thik ad Discuss Geometric Sequece -- Commo Ratio -- Are the give sequeces geometric? If so idetify the commo ratio. {5,15,5,135,...} {15,30,5,0,...} What is the 10th term i the sequece, a 10, i the first problem? How did you fid it? Explicit Formula -- expresses the term i terms of. Write a explicit formula for the first problem above. Check your formula with the aswer came up for the 10th term. How did you fid the formula? (Hit: What did the graph look like?) Geeral Formula for arithmetic Sequeces --- Try It -- Fid the 19th term of {11,33,99,97,...} Usig your calculator Geometric Mea --- Try it -- Fid the geometric mea betwee ad 3. What if there were two geometric meas? Precalculus Chapter 1 Page 3

4 Series -- expressio for the of the terms i a. How may games are played durig March Madess? Remember you start with teams. Formula -- Try It -- Fid the sum of the series I your first year i the world your mom ad dad started savig for college. They stared with $50 ad each year they deposited 50% more tha the previous year. How much moey will they have i 1 years? Homework: p all, 1-7 all, 9-3 all, 3-38 all, 1,, 7, 9-57 all Precalculus Chapter 1 Page

5 Sectio 1.3 Ifiite Sequeces ad Series Goals: 1. To fid the it of the terms of a ifiite sequece.. To fid the sum of a ifiite geometric series. I. Ifiite Sequeces A. Def A that has a ( ) umbers of terms. B. Develop the rule 1. Calculate:. Rule: x , 000, 000, 000, 000 x C. Examples Fid the it (last term) of each sequece ,,,... 1 Fid: a 3 1. *Hit: 3133,,, Fid: * a ( 1) + 3 II. Ifiite Series A. Def A series of terms together. B. Rules: 1. If r > 1, the S or without boud. C. Examples. If r < 1, the S 1. Fid the sum of the series: A teis ball dropped from a height of feet bouces 50% of the height from which it fell o each bouce. What is the vertical distace it traveled before comig to rest? 3. Write as a fractio. Homework: p all, 5-7 all, 1-3 all, odds, 0,,, -55 all + Worksheet Precalculus Chapter 1 Page 5

6 Goals: 1. To use sigma otio. To use! Sectio 1.5 Sigma Notatio ad! I. Sigma Notatio A. is a Greek capital sigma, it is used like the Eglish S ad is used to represet a series. B. Example 1. Express the series usig sigma otatio.. Write the followig i expaded form ad fid the sum. a) b) k 1 k 1 3 II. Factorial (!) A. Def! B. Examples Write the followig i expaded form ad solve. 1. 5!. 10! 3!! 3. Express the followig series usig sigma otatio: Homework: p , (15-39)/3, 5-8 all, 5-57 all, 59 Precalculus Chapter 1 Page

7 Sectio 1. The Biomial Theorem ad Pascal Triagle Goals: 1. To use the biomial theorem to expad biomials.. To use the Pascal Triagle to expad biomials. I. The Biomial Theorem! r A. Theorem: a b r 0 r!( r)! B. Example 1. ( x+ y) r. 8 (x 3) 3. Fid the th term of (x 3 y) II. Pascal s Triagle A. The triagle: B. Example 1. ( x+ y). 8 (x 3) 3. There are six childre i the Smith family. Of these six childre, there are at least three boys. How may ways ca the Smith family have at least three boys?. Jim has a battig average of.0, which meas he has a failure rate of.70. Write the biomial term for exactly hits i the ext 9 at bats. Compute the percet rate. Homework: p. 803, 11, (1-30)/3, 33, 38- all Precalculus Chapter 1 Page 7