Page 98 - IM_Algebra2_FL Print Sample.pdf

2. Sample response: Sequence C. Term 10 for Sequence C is 1024. Term 10 for Sequence B is 275. Term 10 for Sequence A is 120.
3. Only Sequence C can be geometric. A geometric sequence has the same multiplier from one term to the next, and both Sequences A and B do not have this. Sequence C does; the multiplier is 2.
4. They are all the same, 10.
5. They are not the same, they are increasing multiples of 5.
Activity Synthesis
Ask students how Sequences A and C are alike and di erent. They might o er things like:
• C is geometric but A is not.
• In A, you always add 10 to get from term to term, but in C, you always multiply by 2.
• In C, the constant ratio is 2. In A, you get a constant if you subtract any term from the previous term.
Tell students that Sequence A is an example of an arithmetic sequence. Here are two ways to know a sequence is arithmetic:
• You always add the same number to get from one term to the next.
• If you subtract any term from the next term, you always get the same number.
Share that the constant in an arithmetic sequence is called the common difference. In sequence A, the common di erence is 10, because , , , and .
3.3 A Decreasing Sequence
15 minutes
The purpose of this activity is for students to create another representation of a given sequence, and to give them an opportunity to use new words like sequence, term, arithmetic sequence, and common di erence as they work with the sequence.
Student Task Statement
Here is a graph representing a sequence.
Unit 1 Lesson 3: Di erent Types of Sequences 33