1. 12.2 – Analyze Arithmetic Sequences and Series

2. Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference between any two terms

3. 1. Tell whether the sequence is arithmetic. –4, 1, 6, 11, 16, … +5 Yes +5 a.

4. 1. Tell whether the sequence is arithmetic. 3, 5, 9, 15, 23, … +2+4+6+8 No b.

5. 1. Tell whether the sequence is arithmetic. 17, 14, 11, 8, 5,… –3 Yes –3 c.

6. Rule for an Arithmetic Sequence The nth term of an arithmetic sequence with first term a 1 and common difference d is given by:

7. 2.Write a rule for the nth term of the sequence. Then find a 15. 4, 9, 14, 19, … +5 a. d = 5 a1 =a1 = 4

8. 2.Write a rule for the nth term of the sequence. Then find a 15. 60, 52, 44, 36, … –8 b. d = –8 a1 =a1 = 60

9. 3. Write a rule for the nth term of the sequence given: d = 3, a 19 = 48

10. 4. Write a rule for the nth term of the sequence given: d = –7, a 11 = –57

11. 5. Write a rule for the nth term of the sequence given: a 8 = 21, a 27 = 97 –1

12. 6. Write a rule for the nth term of the sequence given: a 7 = 26, a 16 = 71 –1

13. Arithmetic Series: Adding the terms of an arithmetic sequence

14. Sum of a Finite Arithmetic Series: The sum of the first n terms is:

15. 7. What is the sum of the arithmetic series? a1 =a1 = 3+5(1) a1 =a1 = 8 a 20 = 3+5(20) a 20 = 103 n = 20

16. 8. What is the sum of the arithmetic series? a4 =a4 = 6(4) – 30 a4 =a4 = –6 a9 =a9 = 6(9) – 30 a 20 = 24 n = 6

17. 9. What is the sum of the arithmetic series? a8 =a8 = – 11 + 4(8) a8 =a8 = 21 a 16 = – 11 + 4(16) a 16 = 53 n = 9

18. 10. What is the sum of the arithmetic series? a1 =a1 = 5 an =an = 203 d = 2

19. 11. What is the sum of the arithmetic series? a1 =a1 = 2 an =an = 198 d =7