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Arithmetic Sequences and Series

Arithmetic Sequences and Series. Unit 10.2. 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. Purpose of arithmetic sequence.

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Arithmetic Sequences and Series

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  1. Arithmetic Sequences and Series Unit 10.2

  2. Definition Arithmetic Sequences – A sequence in which the difference between successive terms is a constant. • What is the common difference? • a1 = 22 • a2 = 17 • a3 = 12 • a4 = 7

  3. Purpose of arithmetic sequence Add the common difference to the preceding term. Example d = 3 an=an-1 + d First term a1 = 6 2nd term a2 = a1 + d a2 = 6 + 3 = 9 3rd term a3 = a2 + d a3 = 9 + 3 = 12 4th term a4 = a3 + d a4 = 12 + 3 = 15

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

  5. Nth term Find the 68th term of the arithmetic sequence 25, 17, 9….. difference or d = 25 – 17 = -8 Formula an = a1 + (n - 1)d = 25 + (68 – 1)-8 = 25 – 536 = - 511

  6. Nth Term Find the first term of the arithmetic sequence for which a25 = 139 and d = ¾ 139 = a1 + (n – 1)d 139 = a1 + (25 – 1)3/4 139 = a1 + 18 121 = a1

  7. Exercises • Page 605 Problems 20 - 24

  8. 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 a1 = 4.3 a6 = 12.8 an = a1 + (n – 1)d 12.8 = 4.3 + (6 - 1)d 12.8 = 4.3 + 5d 8.5 = 5d 1.7 = d

  9. Problems • Page 605 Problems 28 - 31

  10. Sums of arithmetic Series • Find each sum with multiple terms • Sn= n/2(a1 + an) • n = number of terms in the sequence • Partial Sum • Sn= n/2(2a1 + (n -1)d)

  11. Exercises Page 605 46 - 53

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