SEQUENCES AND SERIES

Rows is an arrangement of numbers formed by a sequence ofparticular. Numbers are arranged is called interest. Changes among tribessequence determined by ketambahan certain number or a multiple numberparticular.If the row has an additional interest berurutannya a fixed number,then the sequence is called arithmetic. For example:a. 2, 5, 8, 11, 14, ................ plus 3 of the tribe in front of himb. 100, 95, 90, 85, 80, ........ minus 5 from the tribe in front of himIf the sequences have multiple interest berurutannya fixed number, then it is calledgeometric sequence. For example:a. 2, 4, 8, 16, 32, 64, 128, .......... multiplied by 2 of the tribe in front of himb. 80, 40, 20, 10, 5, 2 ½, ............ multiplied by ½ of the tribe in front of himSeries is the sum of the numbers in a row. For example:Arithmetic progression (arithmetically): 2 + 4 + 6 + 8 + 10 = 30Geometric (geometric progression): 2 + 4 + 8 + 16 + 32 = 62Arithmetic sequence and seriesRows of ArithmeticFor example: 2, 5, 8, 11, 14, ......... ana1 = 2 = aa2 = 5 = 2 + 3 = a + ba3 = 8 = 5 + 3 = (a + b) + b = a + 2ba4 = 11 = 8 + 3 = (a + 2b) + b = a + 3ban = a + (n-1) bSo the formula of the n the arithmetic sequence is:aa (n 1) bn 1 = + - or S a (n 1) bn 1 = + - where:Sn = an n-th = Interesta1 = the first termb = different ethnicn = number of termsExercise:1. Look for the tribe to-10 from the line 3, 7, 11, 15, 19, .................2. Tribe to tribe-3 and 16 of the arithmetic sequence is 13 and 78. Determine interestThe first and the difference!Hand out Business Mathematics 183. Look for the 21 tribes into the arithmetic sequence where the tribe 5th = 41 and spare the11 = 23Arithmetic series (Series Count)Eg: Dn = a + (a + b) + (a + 2b) + ........... + (Sn - 2b) + (Sn - b) + SnDn = Sn + (Sn - b) + (Sn - 2b) + ...... + (a + 2b) + (a + b) + a+2 Dn = (a + Sn) + (a + Sn) + (a + Sn) + ................... n2 Dn = n (a + Sn)(A S)2nD n n = + or(A a (n-1) b)2nDn = + +(2a (n - 1) b)2nDn = + whereDn = n-th series (the amount up to the n-th)Exercise:1. Look for the number ten first term of arithmetic sequence: 3, 7, 11, 15, .........2. There are 60 terms in the arithmetic sequence where the first term is 9 andlast tribe is 127. Determine D60!SEQUENCES AND SERIES GEOMETRYBarisan GeometryFor example: 3, 6, 12, 24, 48, .................a1 = 3 = aa2 = 6 = 3 x 2 = a x r = ara3 = 12 = 6 x 2 = x r = ar ar2a4 = 24 = 12 x 2 = ar2 x r = AR3an = arn-1So the formula for n-th in the geometric sequence is:n 1n a = ar - where:an = nth (Sn)a = the first termr = ratio between successive interestn = number of termsHand out Business Mathematics 19Exercise:1. Look for-8 from the tribe to the geometric sequence if the tribe first 16 and the ratiois 2.2. Look for the tribe to-11 in a geometric progression in which the tribe to-4 is 24 andtribes to-9 is 768Series Geometry (Series Measure)Eg: Dn = a + ar + ar2 + AR3 + ............ + Arn-1Dn = r + ar + ar2 + AR3 ............ + Arn-1 + arn-Dn - RDN = a - arn(1-r) Dn = a (1-rn)(1 r)a (1 r)Dnn --= Where:Dn = n-th series (the amount up to the n-th)Exercise:1. Look for the amount up to the tribe to-8 the first of a geometric sequence: 3, 6,12, 24, ........2. If the interest rate the 3rd and 7th of a geometrical progression is 800 eachand 204,800, what is the first term (a), the ratio (r), the tribe to-5 (S5) and the number 5first term (D5)?