Geometric Sequences

1. Geometric Sequences Lesson 9-7

2. Vocabulary • Geometric Sequence – a sequence in which the common ratio is the same • Common Ratio – the ratio between consecutive terms

3. Things to Know • Each term is found by multiplying the previous term by the common ratio. • The common ratio is found by dividing the 2nd term from the 1st term. • Divide the 3rd term from the 2nd term to make sure the common difference is the same.

4. Things to Know • When the terms of a geometric sequence are increasing, the common ratio is greater than 1. • When the terms of a geometric sequence are decreasing, the common ratio is greater than 0 and less than 1.

5. Example 1 Find the common ratio of each geometric sequence. • 1, 3, 9, 27 • 32, 8, 2, ½ • 5, 40, 320, 2560

6. Your Turn Find the common ratio of the geometric sequence. • 5, 30, 180, 1080, …. • 0.5, 1, 2, 4, …. • 16, 8, 4, 2, …. • 9, 3, 1, 1/3, ….

7. Example 2 Write the next three terms of the geometric sequence. • 0.2, 1, 5, 25, …. • 200, 20, 2, 0.2, ….

8. Your Turn Write the next three terms of the geometric sequence. • 6, 12, 24, 48, …. • 160, 80, 40, 20, …. • ½, 1/6, 1/18, 1/54, ….

9. Example 3 During a routine, band members march onto a field as shown. Describe the pattern of the total number of band members on the field as each row marches onto the field. Is the sequence arithmetic, geometric, or neither? Explain.

10. Example 4 In a parade, firemen form rows with 5 men in each row. Describe the pattern in the total number of firemen as each row forms. Is the sequence arithmetic, geometric, or neither? Explain.

11. Your Turn Describe the pattern in the sequence. Then identify the sequence as arithmetic, geometric, or neither. • 0, 11, 22, 33, …. • 1, 3, 7, 13, …. • 0.1, 2, 40, 800, …. • In example 3, how many band members are on the field when there are five rows on the field?

12. Assignment • Page 432-433 #2-24 even in Green Textbook