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Activity Synthesis
For each sequence, invite a student to share how they completed the sequence and determined the common ratio. Highlight the method of dividing any term by the previous term to nd the common ratio. Emphasize that the presence of a common ratio is what makes a sequence a geometric sequence.
Emphasize that the common ratio is de ned to be the multiplier from one term to the next; said another way, the quotient of a term and the previous term. For example, many students will want to say that the pattern of the third sequence is “divide by 10 each time.” This is true, but the common ratio is .
Lesson Synthesis
Ask students to discuss each question with a partner:
• Come up with an example of a geometric sequence.
• What makes it a geometric sequence?
• What is its common ratio?
• (Time permitting) Find the next term and the common ratio for the geometric sequence: 64, 16, 4, . . .
• What parts of this lesson, if any, seemed the most challenging?
Invite students to share anything they are worried about. For example, they might worry about remembering how to know the common ratio of geometric sequences that decrease. It is helpful to keep de nitions in mind. To nd the common ratio, divide any term by the previous term. The common ratio is the number you multiply each term by to get the next term.
2.4 A Possible Geometric Sequence
Cool Down: 5 minutes
Student Task Statement
Here is a sequence: 500, 100, 20, . . .
1. Explain why this sequence could be a geometric sequence.
2. If it is a geometric sequence, what is the next term? 3. What is the common ratio?
Student Response
1. Sample response: The given terms have a common ratio. and each equal . 2. 4
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Teacher Guide
Algebra