1. 8-6: Geometric Sequences Objectives: 1.To form geometric sequences 2.To use formulas when describing geometric sequences.

2. Find the common difference of each sequence. 1.1, 3, 5, 7,...2.19, 17, 15, 13,... 3.1.3, 0.1, –1.1, –2.3,...4.18, 21.5, 25, 28.5,... Use inductive reasoning to find the next two numbers in each pattern. 5.2, 4, 8, 16,...6.4, 12, 36,... Check Skills/Warm Ups

3. 1.1, 3, 5, 7,...2.19, 17, 15, 13,... 7 – 5 = 2, 5 – 3 = 2, 3 – 1 = 213 – 15 = –2, 15 – 17 = –2, Common difference: 217 – 19 = –2 Common difference: –2 3.1.3, 0.1, –1.1, –2.3,...4.18, 21.5, 25, 28.5,... –2.3 – (–1.1) = –1.2, –1.128.5 – 25 = 3.5, 25 – 21.5 = 3.5, – 0.1 = –1.2, 0.1 – 1.3 = –1.221.5 – 18 = 3.5 Common difference: –1.2Common difference: 3.5 5.2, 4, 8, 16,...6.4, 12, 36,... 2(2) = 4, 4(2) = 8, 8(2) = 16,4(3) = 12, 12(3) = 36, 16(2) = 32, 32(2) = 64 36(3) = 108, 108(3) = 324 Next two numbers: 32, 64 Next two numbers: 108, 324 Solutions:

4. Questions??

5. pages 413–416 Exercises 2.c 10 4.q 100 6.d 15 8.x 7 10. 1024m 5 12. 14.81n 24 16.1 18.8x 5 y 3 20. 22. 1 12g 4 1 c 18 a 32 32c 26 24.9  10 10 26.8  10 –9 28.3.6  10 25 30.4.2875  10 –11 HW #39 Solutions

6. Continued

7. 8-6: Geometric Sequences Objectives: 1.To form geometric sequences 2.To use formulas when describing geometric sequences.

8. Key Concepts: Geometric Sequence: a # sequence formed by multiplying a term in a sequence by a fixed # to find the next term. Common Ratio: The fixed # used to find terms in a geometric sequence.

9. Example 1: Find the common ratio of each sequence. a. 3, –15, 75, –375,... 3–1575–375  (–5)  (–5)  (–5) The common ratio is –5. b. 3, 3232 3434 3838,,,... 3 3232 3434 3838  1212  1212  1212 The common ratio is. 1212 Geometric Sequences Multiply each term by (-5) Multiply each term by ( ) 1212

10. Example 2: Find the next three terms of the sequence 5, –10, 20, –40,... 5–1020–40  (–2)  (–2)  (–2) The common ratio is –2. The next three terms are –40(–2) = 80 80(–2) = –160 and –160(–2) = 320 Geometric Sequences Multiply each term by (-2)

11. Example 3: Determine whether each sequence is arithmetic or geometric. a. 162, 54, 18, 6,... 16254186 1313  1313  1313  The sequence has a common ratio (multiplication used) The sequence is geometric. Geometric Sequences

12. Example 3: (continued) b. 98, 101, 104, 107,... The sequence has a common difference. 98101104107 + 3 The sequence is arithmetic. Geometric Sequences

13. Example 4: Find the first, fifth, and tenth terms of the sequence that has the rule A(n) = –3(2) n – 1. first term: A(1) = –3(2) 1 – 1 = –3(2) 0 = –3(1) = –3 fifth term: A(5) = –3(2) 5 – 1 = –3(2) 4 = –3(16) = –48 tenth term: A(10) = –3(2) 10 – 1 = –3(2) 9 = –3(512) = –1536 Geometric Sequences

14. Questions?

15. 1.Find the common ratio of the geometric sequence –3, 6, –12, 24,... 2.Find the next three terms of the sequence 243, 81, 27, 9,... 3.Determine whether each sequence is arithmetic or geometric. a. 37, 34, 31, 28,... b. 8, –4, 2, –1,... 4.Find the first, fifth, and ninth terms of the sequence that has the rule A(n) = 4(5) n–1. –2 3, 1, 1313 arithmetic geometric 4, 2500, 1,562,500 Try These!

16. HW #40: p. 427 #1-24, 55-63