12.2 – Analyze Arithmetic Sequences and Series. Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference.

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Presentation transcript:

12.2 – Analyze Arithmetic Sequences and Series

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

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

1. Tell whether the sequence is arithmetic. 3, 5, 9, 15, 23, … No b.

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

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

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

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

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

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

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

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

Arithmetic Series: Adding the terms of an arithmetic sequence

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

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

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

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

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

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