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Arithmetic Sequences and Series Unit 10.2

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Definition Arithmetic Sequences – A sequence in which the difference between successive terms is a constant. What is the common difference? a 1 = 22 a 2 = 17 a 3 = 12 a 4 = 7

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Purpose of arithmetic sequence Add the common difference to the preceding term. Example d = 3 a n =a n-1 + d First term a 1 = 6 2 nd term a 2 = a 1 + d a 2 = 6 + 3 = 9 3 rd term a 3 = a 2 + d a 3 = 9 + 3 = 12 4 th term a 4 = a 3 + d a 4 = 12 + 3 = 15

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Exercises Unit 10.2 Page 605 Problems 1 – 4 1.d = -3 11, 8, 5, 2 2.d = 13 42, 55, 68, 81 3.d = -9 90, 81, 72, 63 4.d = 22 -17, 5, 27, 49

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Nth term Find the 68 th term of the arithmetic sequence 25, 17, 9….. difference or d = 25 – 17 = -8 Formula a n = a 1 + (n - 1)d = 25 + (68 – 1)-8 = 25 – 536 = - 511

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Nth Term Find the first term of the arithmetic sequence for which a 25 = 139 and d = ¾ 139 = a 1 + (n – 1)d 139 = a 1 + (25 – 1)3/4 139 = a 1 + 18 121 = a 1

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Exercises Page 605 Problems 20 - 24

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Arithmetic Means Write an arithmetic sequence that has four arithmetic means between 4.3 and 12.8 4.3,a, b, c, d, 12.8 a 1 = 4.3 a 6 = 12.8 a n = a 1 + (n – 1)d 12.8 = 4.3 + (6 - 1)d 12.8 = 4.3 + 5d 8.5 = 5d 1.7 = d

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Problems Page 605 Problems 28 - 31

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Sums of arithmetic Series Find each sum with multiple terms S n = n/2(a 1 + a n ) n = number of terms in the sequence Partial Sum S n = n/2(2a 1 + (n -1)d)

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Exercises Page 605 46 - 53

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