Page 100 - IM_Algebra2_FL Print Sample.pdf

4. -4, -8, -12
Activity Synthesis
Ensure students can articulate that this sequence is arithmetic because it has a common di erence.
Lesson Synthesis
Ask students to discuss with a partner: “How are arithmetic and geometric sequences alike and di erent?” After they have had a few minutes to discuss, ask several students to share the things that came up. Some things to highlight:
• They are both types of sequences; that is, they are both lists of numbers.
• To get from one term to the next for both arithmetic and geometric sequences, you “do the
same thing each time.”
• For geometric sequences, you always multiply by the same number to get the next term. For arithmetic sequences, you always add the same number to get the next term.
• Geometric sequences have common ratios (the quotient of any term and the previous term), but arithmetic sequences has common di erences (the di erence of any term and the previous term).
• If you graph each term as a function of the term number, a geometric sequence looks like an exponential function, but an arithmetic term looks like a linear function.
3.4 Do What’s Next
Cool Down: 5 minutes
Student Task Statement
Many sequences start with the terms 3 and 6.
1. Find the next two terms of an arithmetic sequence: 3, 6, __, __.
2. Find the next two terms of a geometric sequence: 3, 6, __, __.
3. Find the next two terms of neither a geometric nor arithmetic sequence: 3, 6, __, __.
Student Response
1. 9, 12
2. 12, 24
3. Sample response: 0, 1
Unit 1 Lesson 3: Di erent Types of Sequences 35