2. Standard Accessed: Students will analyze sequences, find sums of series, and use recursive rules.

3. Warm-up Check 1.Find the next term in each sequence? a. 0, 7, 14, 21, … 28 4 2. A high school graduated 250 seniors in 2004. In 2005 the number of graduating seniors increased by 4%. How many seniors graduated in 2005? 260 Seniors b. 0.25, 0.50, 1, 2, …

4. Big Idea How can you tell that a sequence is geometric? Examine the differences of consecutive terms.

5. Vocabulary The ratio of any term to the previous term is constant. This ratio is denoted by r.r. Is the expression formed by adding the terms of a geometric sequence.

6. Identify geometric sequences EXAMPLE 1 SOLUTION (a)= 6 ÷ 2 = 3 = 18 ÷ 6 = 3 = 54 ÷ 18 = 3 = 162 ÷ 54 = 3 r = 3; Geometric Sequence (b) = 7 ÷ 2 = 7/2 = 12 ÷ 7 = 12/7 No common r; Not Geometric Sequence

7. EXAMPLE 2 SOLUTION

8. Write a rule given a term and a common ratio r. EXAMPLE 3 SOLUTION

9. EXAMPLE 4 SOLUTION Write a rule given two terms.

10. EXAMPLE 5 Finding the Sum of a Finite Geometric Series.

11. Hyundai Cars: EXAMPLE 6 Use an Geometric sequence and series in real life In 1999 about 586 thousand new Hyundai cars were sold in Seoul. From 1999 through 2004, the number of new cars sold increased by about 3.8% per year. b.What was the total number of new cars sold in Seoul from 1999 to 2004?

12. Lesson 7.3 Analyze Geometric Sequences & Series Homework: Honors – Homework Academic – Homework