Ratios, Rates and Percents Lesson 2 Ratios, Rates and Percents Geometric Sequences

Warm-Up Simplify the ratio and write the ratio as a fraction, with a colon, and using the word “to”. The Eagles had a win to loss ratio of 1:1. Explain the ratio’s meaning. Curt had 6 yellow flowers and 8 pink flowers. Write the ratio of yellow flowers to total flowers Curt has.

Target: Recognize and complete geometric sequences.

Vocabulary 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.

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

Example 1b Find the ratio of each geometric sequence. Use the ratio to find the next two terms of the geometric sequence 256, 64, 16, 4… Divide each term by the previous term: The ratio is . Multiply each term by to find the next term: The ratio is and the next two terms are 1 and .

Example 2 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. Multiply each term by 5 to get the next term:

Exit Problems Find the ratio of the geometric sequence 3, 6, 12, 24, 48, … Write the first four terms of a geometric sequence with a first term of 81 and a ratio of . Determine whether or not the sequence given is a geometric sequence. Explain your answer. 4, 8, 12, 16, 20, …

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