PreCalc 9.2 and 9.3.notebook

PreCalc 9.2 and 9.3.notebookMay 04, 20129.2 Arithmetic SequencesArithmetic sequenceA sequence whose consecutive terms have aCommon Difference (d)Formula:an = a1 + (n­1)dEX 1Determine the common difference (d) when the sequence is arithmetic1. 7, 11, 15, 19, 23, ... d=2. 2, ­3, ­8, ­13, ­18,...d=3. 80, 40, 20, 10, 5, ... d=EX 2Find a formula for an for the arithmetic sequence1. a1=10 , d=5 2. a1=­x , d=3xEX 3The first 2 terms of the arithmetic sequence are given.Find the missing term.1. a1=4 , a2=7, a10= 2. a1=11 , a2=9.8, a15=1

PreCalc 9.2 and 9.3.notebook9.2 Arithmetic SequencesA sequence (progression) is arithmetic if the differences betweenconsecutive terms are the same. Terms are found by adding a realnumber constant d, called theFormula to find the n th term:May 04, 2012EX 1 Given the arithmetic sequences below, find a) common differenceb) the specified termc) a formula for a n1. 3,7,11,15,19,...a) d=Common Differencean = a1 + (n­1)d2. 5,2,­1,­4,­7,...a) d=b) find the 10 th termb) find the 120 th termc) find formula for a nc) find formula for a n3. 3, 5, 2, 3, 1, ...2 2a) d=b) find the 15 th termc) find formula for a n2

PreCalc 9.2 and 9.3.notebookMay 04, 2012EX 2Find a formula for a n for each arithmetic sequence:4) a 1 = 10, d = ­4 5) a 1 = ­y, d = 5yEX 3Write the first 5 terms of the arithmetic sequence:6) a 1 = 5, d =­ 347) a 1 = 16.5, d = 0.25Now try in the calculator: a 1 + d EnterCalculator reads:5 + ­ 3Enter 54(Ans) + ­3174 Enter4EnterEnter3

PreCalc 9.2 and 9.3.notebookMay 04, 20128) a 1 = 3, a 15 = 73EX 4 The first two terms of the arithmetic sequence are given.Find the missing term:9) a 1 =3, a 2 =13, a 9 = 10) a 1 =9.2, a 2 =6.6, a 32 =EX 5 Find the Partial Sum:11) 1002x ­ 812)Σ x=05100 50Σ Σn=51n­n=1=n=STOPHW pg 650: 100,102pg 659: Do only odd problems1­7, 11­15, 19­25, 31­35, 39,41, 45, 47, 67­794

PreCalc 9.2 and 9.3.notebookMay 04, 20129.3 Geometric Sequences/Series9.3 p1In a geometric sequence(progression), terms are obtained bymultiplying by a nonzero real number constant r, called theCommon Ratio The formula is an = a1(r) n­1EX 1Determine whether the sequence is(A) Arithmetic, (G) Geomteric, or (N) Neither.Find d if arithmetic, r if geometric.1. 10, 8, 6, 4, 2,...4. 1 , 2 , 1 , 4 , 5 ,...3 3 3 62. 80, 40, 20, 10, 5,...5. 5, 15, 45, 135,...3. 1 , 2 , 4 , 8 , 16 ,...3 3 3 3 36. 1 , ­1 , 1 , ­1,...2 4 86

PreCalc 9.2 and 9.3.notebookMay 04, 20129.3 p2EX 4 Find the indicated n th term of the geometric sequence:12) 9th term: 6,18,54,... 13) 10th term: 3,12,48,...EX 5 Find the sum of the finite geometric sequence/series:NO CALC for 14 and 15:514)Σ10( 1 ) n =5 n=0415)Σn=1=5( ­ 3 ) n­1 =2=WITH A CALC for 16 and 17:1016)Σn=16Σ17)n=05( ) n­1 2= ________________500(1.04) n = _______________8

PreCalc 9.2 and 9.3.notebookMay 04, 201220.∞5(1 ) k­1Σk=12 =21.Σn=0∞3( )250.2n=22522. 2 + + +2125 + ...23. 4 + 2 + 1 + 1 +214+...STOPHW pg 669:2­20 EV, 27, 28, 30, 32,53, 57, 59 ( No Calc)61, 65, 69 (Using a Calc)80­90 EV10