1. Geometric Sequences Lesson 1.2 Core Focus on Ratios, Rates and Statistics

2. 1.Simplify the ratio and write the ratio as a fraction, with a colon and using the word “to”. 2.The Eagles had a win to loss ratio of 1 : 1. Explain the ratio’s meaning. 3.Curt had 6 yellow flowers and 8 pink flowers. Write the ratio of yellow flowers to total flowers Curt has. Warm-Up For every 1 win the team had 1 loss. (The same number of wins as losses.)

3. Geometric Sequences Recognize and complete geometric sequences. Lesson 1.2

4. Sequence An ordered list of numbers. Term A number in a sequence. Geometric Sequence A list of numbers created by multiplying the previous term in the sequence by a common ratio. Good to Know! The number you multiply by each time to get the next term is the ratio between the terms. The ratio can also be determined by writing the ratio of each term to its previous term. Vocabulary 124816 1 st term 2 nd term 3 rd term 4 th term 5 th term 22 22 22 22

5. Find the ratio of each geometric sequence. Use the ratio to find the next two terms of the geometric sequence. a.1, 3, 9, 27, … The find the ratio, divide one term by the previous term. The ratio is 3. Find the next two terms by multiplying27  3 = 81 81  3 = 243 the previous term by 3. The next two terms are 81 and 243. Example 1

6. Find the ratio of each geometric sequence. Use the ratio to find the next two terms of the geometric sequence. b.256, 64, 16, 4, … The find the ratio, divide one term by the previous term. The ratio is. Find the next two terms by multiplying the previous term by. The next two terms are 1 and. Example 1 Continued…

7. One geometric sequence begins with the number 2. Another begins with the number 3. Each geometric sequence has a ratio of 5. Write the first five terms of each geometric sequence. Since the ratio of both geometric sequences is 5, multiply each term in the sequence by 5 to get the next term. The geometric sequences are: 2, 10, 50, 250, 1250, …and3, 15, 75, 375, 1875, … Example 2 55 55 55 55 55 55 55 55

8. Step 1Find the next two numbers in each sequence (A–E) above. Step 2Explain how you found the next two numbers in each sequence. Step 3a.Identify which sequences (A–E) are geometric sequences. b.Find the first term of each geometric sequence. c. Find the ratio of each geometric sequence. Step 4An arithmetic sequence is formed when the same number is added to a term to find the next term. a.Which sequences (A–E) are arithmetic sequences? b.Do arithmetic sequences have the same ratio between terms? Explain using examples. Step 5Write the first five terms of your own geometric sequence. Identify the first term and the ratio of the sequence.

9. How can you identify a geometric sequence if you are given a list of numbers? Communication Prompt

10. 1.Find the ratio of the geometric sequence 3, 6, 12, 24, 48, … 2.Write the first four terms of a geometric sequence with a first term of 81 and a ratio of. 3.Determine whether or not the sequence given is a geometric sequence. Explain your answer. 4, 8, 12, 16, 20, … Exit Problems 2 81, 27, 9, 3 Not geometric because and. These ratios are not equal.